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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 20449b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20449.d1 | 20449b1 | \([0, -1, 1, -27265, 6317794]\) | \(-262144/1859\) | \(-15896284050080291\) | \([]\) | \(80640\) | \(1.7919\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 20449b1 has rank \(0\).
Complex multiplication
The elliptic curves in class 20449b do not have complex multiplication.Modular form 20449.2.a.b
sage: E.q_eigenform(10)