# Properties

 Label 9408da Number of curves $4$ Conductor $9408$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("da1")

sage: E.isogeny_class()

## Elliptic curves in class 9408da

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
9408.cb3 9408da1 $$[0, 1, 0, -604, -4978]$$ $$3241792/567$$ $$4269246912$$ $$$$ $$6144$$ $$0.56775$$ $$\Gamma_0(N)$$-optimal
9408.cb2 9408da2 $$[0, 1, 0, -2809, 51911]$$ $$5088448/441$$ $$212513624064$$ $$[2, 2]$$ $$12288$$ $$0.91432$$
9408.cb1 9408da3 $$[0, 1, 0, -43969, 3534047]$$ $$2438569736/21$$ $$80957571072$$ $$$$ $$24576$$ $$1.2609$$
9408.cb4 9408da4 $$[0, 1, 0, 3071, 245951]$$ $$830584/7203$$ $$-27768446877696$$ $$$$ $$24576$$ $$1.2609$$

## Rank

sage: E.rank()

The elliptic curves in class 9408da have rank $$0$$.

## Complex multiplication

The elliptic curves in class 9408da do not have complex multiplication.

## Modular form9408.2.a.da

sage: E.q_eigenform(10)

$$q + q^{3} - 2 q^{5} + q^{9} + 4 q^{11} - 6 q^{13} - 2 q^{15} + 2 q^{17} + 4 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.
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