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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 19950p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
19950.e1 | 19950p1 | \([1, 1, 0, -12105, -3294675]\) | \(-1569510182075597/36491419872936\) | \(-4561427484117000\) | \([]\) | \(153216\) | \(1.6854\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 19950p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 19950p do not have complex multiplication.Modular form 19950.2.a.p
sage: E.q_eigenform(10)