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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 166635.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
166635.b1 | 166635j1 | \([0, 0, 1, -398613, 135474318]\) | \(-18163305455448064/10048419997875\) | \(-3875082736400512875\) | \([]\) | \(4193280\) | \(2.2702\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 166635.b1 has rank \(1\).
Complex multiplication
The elliptic curves in class 166635.b do not have complex multiplication.Modular form 166635.2.a.b
sage: E.q_eigenform(10)