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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 51870i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
51870.f1 | 51870i1 | \([1, 1, 0, -162858, -343886508]\) | \(-477699921678975260329/50790819477557053440\) | \(-50790819477557053440\) | \([]\) | \(2534400\) | \(2.4607\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 51870i1 has rank \(1\).
Complex multiplication
The elliptic curves in class 51870i do not have complex multiplication.Modular form 51870.2.a.i
sage: E.q_eigenform(10)