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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 42135h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
42135.g1 | 42135h1 | \([0, 1, 1, -621725, -189502969]\) | \(-1199124250624/4471875\) | \(-99116252423746875\) | \([]\) | \(505440\) | \(2.1212\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 42135h1 has rank \(1\).
Complex multiplication
The elliptic curves in class 42135h do not have complex multiplication.Modular form 42135.2.a.h
sage: E.q_eigenform(10)