Properties

Label 77616.bz
Number of curves 4
Conductor 77616
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("77616.bz1")
sage: E.isogeny_class()

Elliptic curves in class 77616.bz

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
77616.bz1 77616gn4 [0, 0, 0, -1033851, -404211094] 2 884736  
77616.bz2 77616gn2 [0, 0, 0, -81291, -2802310] 4 442368  
77616.bz3 77616gn1 [0, 0, 0, -46011, 3766826] 2 221184 \(\Gamma_0(N)\)-optimal
77616.bz4 77616gn3 [0, 0, 0, 306789, -21818230] 2 884736  

Rank

sage: E.rank()

The elliptic curves in class 77616.bz have rank \(1\).

Modular form 77616.2.a.bz

sage: E.q_eigenform(10)
\( q - 2q^{5} + q^{11} + 2q^{13} - 2q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.