Properties

Label 94640.bz
Number of curves $4$
Conductor $94640$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("94640.bz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 94640.bz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
94640.bz1 94640cj4 [0, 0, 0, -723827, 237016754] [2] 737280  
94640.bz2 94640cj3 [0, 0, 0, -237107, -41527694] [2] 737280  
94640.bz3 94640cj2 [0, 0, 0, -47827, 3255954] [2, 2] 368640  
94640.bz4 94640cj1 [0, 0, 0, 6253, 303186] [2] 184320 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 94640.bz have rank \(1\).

Modular form 94640.2.a.bz

sage: E.q_eigenform(10)
 
\( q + q^{5} - q^{7} - 3q^{9} + 4q^{11} + 2q^{17} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.