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SageMath
E = EllipticCurve("s1")
E.isogeny_class()
Elliptic curves in class 82810.s
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
82810.s1 | 82810c1 | \([1, -1, 0, 1405, -28798379]\) | \(219083319/256000000000\) | \(-358269184000000000\) | \([]\) | \(1035504\) | \(2.0472\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 82810.s1 has rank \(0\).
Complex multiplication
The elliptic curves in class 82810.s do not have complex multiplication.Modular form 82810.2.a.s
sage: E.q_eigenform(10)