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SageMath
E = EllipticCurve("v1")
E.isogeny_class()
Elliptic curves in class 68544.v
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
68544.v1 | 68544bq2 | \([0, 0, 0, -4716, -54864]\) | \(60698457/28322\) | \(5412418486272\) | \([2]\) | \(98304\) | \(1.1377\) | |
68544.v2 | 68544bq1 | \([0, 0, 0, 1044, -6480]\) | \(658503/476\) | \(-90965016576\) | \([2]\) | \(49152\) | \(0.79117\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 68544.v have rank \(1\).
Complex multiplication
The elliptic curves in class 68544.v do not have complex multiplication.Modular form 68544.2.a.v
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.