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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 8325.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8325.e1 | 8325x1 | \([0, 0, 1, -225, -844]\) | \(110592/37\) | \(421453125\) | \([]\) | \(3584\) | \(0.35748\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8325.e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 8325.e do not have complex multiplication.Modular form 8325.2.a.e
sage: E.q_eigenform(10)