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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 61347.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
61347.p1 | 61347g1 | \([0, -1, 1, -66609209, -209220120484]\) | \(-462482914449031168/3326427\) | \(-235076302748106963\) | \([]\) | \(5225472\) | \(2.9300\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 61347.p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 61347.p do not have complex multiplication.Modular form 61347.2.a.p
sage: E.q_eigenform(10)