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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 3450.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
3450.e1 | 3450g1 | \([1, 1, 0, -3450, 76500]\) | \(11631015625/13248\) | \(5175000000\) | \([]\) | \(2880\) | \(0.77723\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 3450.e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 3450.e do not have complex multiplication.Modular form 3450.2.a.e
sage: E.q_eigenform(10)