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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 200400p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
200400.ce1 | 200400p1 | \([0, 1, 0, -1305408, -575332812]\) | \(-3843995587427449/6390046584\) | \(-408962981376000000\) | \([]\) | \(3386880\) | \(2.2753\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 200400p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 200400p do not have complex multiplication.Modular form 200400.2.a.p
sage: E.q_eigenform(10)