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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 100018.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100018.b1 | 100018b1 | \([1, 1, 0, -50, -172]\) | \(-14260515625/1600288\) | \(-1600288\) | \([]\) | \(26240\) | \(-0.072382\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 100018.b1 has rank \(0\).
Complex multiplication
The elliptic curves in class 100018.b do not have complex multiplication.Modular form 100018.2.a.b
sage: E.q_eigenform(10)