Properties

Label 77.c
Number of curves 2
Conductor 77
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("77.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 77.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
77.c1 77c2 [1, 1, 0, -51, 110] [2] 12  
77.c2 77c1 [1, 1, 0, 4, 11] [2] 6 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 77.c have rank \(0\).

Modular form 77.2.a.c

sage: E.q_eigenform(10)
 
\( q + q^{2} + 2q^{3} - q^{4} - 2q^{5} + 2q^{6} - q^{7} - 3q^{8} + q^{9} - 2q^{10} + q^{11} - 2q^{12} + 4q^{13} - q^{14} - 4q^{15} - q^{16} + 4q^{17} + q^{18} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.