# Properties

 Label 94640cx Number of curves $3$ Conductor $94640$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("cx1")

sage: E.isogeny_class()

## Elliptic curves in class 94640cx

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
94640.be2 94640cx1 $$[0, -1, 0, -3605, -91235]$$ $$-262144/35$$ $$-691971338240$$ $$[]$$ $$98496$$ $$1.0045$$ $$\Gamma_0(N)$$-optimal
94640.be3 94640cx2 $$[0, -1, 0, 23435, 227837]$$ $$71991296/42875$$ $$-847664889344000$$ $$[]$$ $$295488$$ $$1.5538$$
94640.be1 94640cx3 $$[0, -1, 0, -355125, 85328125]$$ $$-250523582464/13671875$$ $$-270301304000000000$$ $$[]$$ $$886464$$ $$2.1031$$

## Rank

sage: E.rank()

The elliptic curves in class 94640cx have rank $$0$$.

## Complex multiplication

The elliptic curves in class 94640cx do not have complex multiplication.

## Modular form 94640.2.a.cx

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{7} - 2q^{9} - 3q^{11} - q^{15} + 3q^{17} + 2q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 