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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 100029.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100029.b1 | 100029a1 | \([0, -1, 1, -64, 165]\) | \(29446377472/8102349\) | \(8102349\) | \([]\) | \(35160\) | \(0.033195\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 100029.b1 has rank \(1\).
Complex multiplication
The elliptic curves in class 100029.b do not have complex multiplication.Modular form 100029.2.a.b
sage: E.q_eigenform(10)