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SageMath
E = EllipticCurve("dx1")
E.isogeny_class()
Elliptic curves in class 47040.dx
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
47040.dx1 | 47040cr1 | \([0, 1, 0, -3201, -4911201]\) | \(-392/1125\) | \(-10413167579136000\) | \([]\) | \(354816\) | \(1.7524\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 47040.dx1 has rank \(1\).
Complex multiplication
The elliptic curves in class 47040.dx do not have complex multiplication.Modular form 47040.2.a.dx
sage: E.q_eigenform(10)