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SageMath
E = EllipticCurve("cm1")
E.isogeny_class()
Elliptic curves in class 75456cm
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
75456.bj1 | 75456cm1 | \([0, 0, 0, -495948, 133068944]\) | \(70593496254289/824180736\) | \(157503391411470336\) | \([]\) | \(774144\) | \(2.1121\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 75456cm1 has rank \(1\).
Complex multiplication
The elliptic curves in class 75456cm do not have complex multiplication.Modular form 75456.2.a.cm
sage: E.q_eigenform(10)