# Properties

 Label 116242x Number of curves $2$ Conductor $116242$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("x1")

sage: E.isogeny_class()

## Elliptic curves in class 116242x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116242.o2 116242x1 $$[1, 0, 0, 12447, -2513207]$$ $$4533086375/60669952$$ $$-2854271342067712$$ $$$$ $$733824$$ $$1.6464$$ $$\Gamma_0(N)$$-optimal
116242.o1 116242x2 $$[1, 0, 0, -218593, -36845751]$$ $$24553362849625/1755162752$$ $$82573177966224512$$ $$$$ $$1467648$$ $$1.9930$$

## Rank

sage: E.rank()

The elliptic curves in class 116242x have rank $$0$$.

## Complex multiplication

The elliptic curves in class 116242x do not have complex multiplication.

## Modular form 116242.2.a.x

sage: E.q_eigenform(10)

$$q + q^{2} - 2q^{3} + q^{4} - 2q^{6} + q^{7} + q^{8} + q^{9} + 4q^{11} - 2q^{12} + q^{14} + q^{16} + 6q^{17} + q^{18} + O(q^{20})$$ ## Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the Cremona numbering.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.
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