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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 82800.x
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
82800.x1 | 82800dj1 | \([0, 0, 0, -190200, 44741500]\) | \(-260956266496/145546875\) | \(-424414687500000000\) | \([]\) | \(1032192\) | \(2.0858\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 82800.x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 82800.x do not have complex multiplication.Modular form 82800.2.a.x
sage: E.q_eigenform(10)