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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 225318.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
225318.r1 | 225318h1 | \([1, 1, 1, -1491072285185, 700802714776192661]\) | \(-15397029525197722850243627281/15665817798\) | \(-373023278379095479822278\) | \([]\) | \(4152844800\) | \(5.1945\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 225318.r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 225318.r do not have complex multiplication.Modular form 225318.2.a.r
sage: E.q_eigenform(10)