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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 21780.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
21780.p1 | 21780bb1 | \([0, 0, 0, -4727712, 4285772084]\) | \(-292124360704/29296875\) | \(-1172007181867500000000\) | \([]\) | \(887040\) | \(2.7830\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 21780.p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 21780.p do not have complex multiplication.Modular form 21780.2.a.p
sage: E.q_eigenform(10)