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SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 49725.q
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
49725.q1 | 49725w1 | \([0, 0, 1, -9000, -324844]\) | \(283115520/3757\) | \(1069864453125\) | \([]\) | \(67200\) | \(1.1155\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 49725.q1 has rank \(2\).
Complex multiplication
The elliptic curves in class 49725.q do not have complex multiplication.Modular form 49725.2.a.q
sage: E.q_eigenform(10)