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SageMath
E = EllipticCurve("p1")
E.isogeny_class()
Elliptic curves in class 83400.p
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
83400.p1 | 83400h1 | \([0, 1, 0, 117, 738]\) | \(702464/1251\) | \(-312750000\) | \([]\) | \(40320\) | \(0.31490\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 83400.p1 has rank \(1\).
Complex multiplication
The elliptic curves in class 83400.p do not have complex multiplication.Modular form 83400.2.a.p
sage: E.q_eigenform(10)