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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 198900r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
198900.ch1 | 198900r1 | \([0, 0, 0, -3225, 82825]\) | \(-508844800/112047\) | \(-816822630000\) | \([]\) | \(248832\) | \(1.0063\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 198900r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 198900r do not have complex multiplication.Modular form 198900.2.a.r
sage: E.q_eigenform(10)