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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 177870.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
177870.p1 | 177870in1 | \([1, 1, 0, -395518, 96982978]\) | \(-164871161098277623/2824295364810\) | \(-117216730525709430\) | \([]\) | \(2672640\) | \(2.0735\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 177870.p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 177870.p do not have complex multiplication.Modular form 177870.2.a.p
sage: E.q_eigenform(10)