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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 257754.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
257754.p1 | 257754p1 | \([1, 1, 0, -163901, -55446723]\) | \(-28671066937/61415424\) | \(-1043052725193744384\) | \([]\) | \(3983616\) | \(2.1463\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 257754.p1 has rank \(0\).
Complex multiplication
The elliptic curves in class 257754.p do not have complex multiplication.Modular form 257754.2.a.p
sage: E.q_eigenform(10)