Properties

Label 77616gi
Number of curves 2
Conductor 77616
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("77616.fw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 77616gi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
77616.fw2 77616gi1 [0, 0, 0, 1176, 8575] [2] 69120 \(\Gamma_0(N)\)-optimal
77616.fw1 77616gi2 [0, 0, 0, -5439, 73402] [2] 138240  

Rank

sage: E.rank()
 

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

Modular form 77616.2.a.fw

sage: E.q_eigenform(10)
 
\( q + 2q^{5} + q^{11} + 2q^{13} + 4q^{17} - 6q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.