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SageMath
E = EllipticCurve("bi1")
E.isogeny_class()
Elliptic curves in class 82810bi
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
82810.o1 | 82810bi1 | \([1, 1, 0, -2443067, -1485239699]\) | \(-1182740881/13520\) | \(-18433899082513962320\) | \([]\) | \(2935296\) | \(2.5105\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 82810bi1 has rank \(1\).
Complex multiplication
The elliptic curves in class 82810bi do not have complex multiplication.Modular form 82810.2.a.bi
sage: E.q_eigenform(10)