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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 76664.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76664.c1 | 76664f1 | \([0, 0, 0, -13690, 455877]\) | \(6912000/1813\) | \(74426591672272\) | \([2]\) | \(153216\) | \(1.3705\) | \(\Gamma_0(N)\)-optimal |
76664.c2 | 76664f2 | \([0, 0, 0, 34225, 2937874]\) | \(6750000/9583\) | \(-6294363181426432\) | \([2]\) | \(306432\) | \(1.7171\) |
Rank
sage: E.rank()
The elliptic curves in class 76664.c have rank \(0\).
Complex multiplication
The elliptic curves in class 76664.c do not have complex multiplication.Modular form 76664.2.a.c
sage: E.q_eigenform(10)
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.