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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 82810.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
82810.k1 | 82810bh1 | \([1, 1, 0, -36353762, 84378900754]\) | \(-27279055902727/10156250\) | \(-1978225777227202343750\) | \([]\) | \(7827456\) | \(3.0536\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 82810.k1 has rank \(1\).
Complex multiplication
The elliptic curves in class 82810.k do not have complex multiplication.Modular form 82810.2.a.k
sage: E.q_eigenform(10)