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SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 82810bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
82810.p1 | 82810bn1 | \([1, 1, 0, 993548, 1213662416]\) | \(86938307/560000\) | \(-698660898171083120000\) | \([]\) | \(5031936\) | \(2.6814\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 82810bn1 has rank \(0\).
Complex multiplication
The elliptic curves in class 82810bn do not have complex multiplication.Modular form 82810.2.a.bn
sage: E.q_eigenform(10)