# Properties

 Label 46410e Number of curves 1 Conductor 46410 CM no Rank 1

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("46410.e1")

sage: E.isogeny_class()

## Elliptic curves in class 46410e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
46410.e1 46410e1 [1, 1, 0, -92228, -47906022] [] 1108800 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curve 46410e1 has rank $$1$$.

## Modular form 46410.2.a.e

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{7} - q^{8} + q^{9} + q^{10} + 6q^{11} - q^{12} + q^{13} + q^{14} + q^{15} + q^{16} + q^{17} - q^{18} + q^{19} + O(q^{20})$$
{"ft_lang_label":"__label__en","ft_lang_prob":0.5010215,"math_prob":0.9992828,"size":450,"snap":"2019-51-2020-05","text_gpt3_token_len":175,"char_repetition_ratio":0.14349777,"word_repetition_ratio":0.0,"special_character_ratio":0.40444446,"punctuation_ratio":0.24418604,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9991178,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-12-07T00:57:24Z\",\"WARC-Record-ID\":\"<urn:uuid:ed908b42-14af-41c5-b195-7bd419b27090>\",\"Content-Length\":\"17780\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:cb0c1461-dc9d-4dbd-b563-2334fea8e756>\",\"WARC-Concurrent-To\":\"<urn:uuid:4d08b31e-3245-4422-8337-2c55a43c7fe9>\",\"WARC-IP-Address\":\"35.241.19.59\",\"WARC-Target-URI\":\"https://www.lmfdb.org/EllipticCurve/Q/46410e/\",\"WARC-Payload-Digest\":\"sha1:V5C72KK5P2OJDCOJIABY74UO6UZV4HRB\",\"WARC-Block-Digest\":\"sha1:DYSOXF7BJ4OKV2BELMLLXKIDGC4TWHKM\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-51/CC-MAIN-2019-51_segments_1575540491871.35_warc_CC-MAIN-20191207005439-20191207033439-00558.warc.gz\"}"}