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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 4200s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4200.m1 | 4200s1 | \([0, -1, 0, -8, 57]\) | \(-160000/3087\) | \(-1234800\) | \([]\) | \(576\) | \(-0.15014\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4200s1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4200s do not have complex multiplication.Modular form 4200.2.a.s
sage: E.q_eigenform(10)