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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 200400.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
200400.p1 | 200400dd1 | \([0, -1, 0, 1717, 14562]\) | \(2237904896/1690875\) | \(-422718750000\) | \([]\) | \(184320\) | \(0.91899\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 200400.p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 200400.p do not have complex multiplication.Modular form 200400.2.a.p
sage: E.q_eigenform(10)