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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 42350i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
42350.k1 | 42350i1 | \([1, 1, 0, -996250, 382416500]\) | \(-57839429434456681/16470860000\) | \(-31140219687500000\) | \([]\) | \(645120\) | \(2.1454\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 42350i1 has rank \(0\).
Complex multiplication
The elliptic curves in class 42350i do not have complex multiplication.Modular form 42350.2.a.i
sage: E.q_eigenform(10)