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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 19650n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19650.q1 | 19650n1 | \([1, 0, 1, -21526, 1201448]\) | \(70593496254289/824180736\) | \(12877824000000\) | \([]\) | \(70560\) | \(1.3278\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 19650n1 has rank \(1\).
Complex multiplication
The elliptic curves in class 19650n do not have complex multiplication.Modular form 19650.2.a.n
sage: E.q_eigenform(10)