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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 27225bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
27225.p1 | 27225bn1 | \([1, -1, 1, -2630, -111878]\) | \(-1459161/3125\) | \(-4307080078125\) | \([]\) | \(40320\) | \(1.1132\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 27225bn1 has rank \(1\).
Complex multiplication
The elliptic curves in class 27225bn do not have complex multiplication.Modular form 27225.2.a.bn
sage: E.q_eigenform(10)