Properties

Label 94640.be
Number of curves $3$
Conductor $94640$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("be1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 94640.be

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

Rank

sage: E.rank()
 

The elliptic curves in class 94640.be have rank \(0\).

Complex multiplication

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

Modular form 94640.2.a.be

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{7} - 2q^{9} - 3q^{11} - q^{15} + 3q^{17} + 2q^{19} + O(q^{20})\)  Toggle raw display

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.