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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 450840e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
450840.e1 | 450840e1 | \([0, -1, 0, -3856801, -26984195195]\) | \(-1026767289066496/50316682419315\) | \(-310917732799309502780160\) | \([]\) | \(61102080\) | \(3.1878\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 450840e1 has rank \(0\).
Complex multiplication
The elliptic curves in class 450840e do not have complex multiplication.Modular form 450840.2.a.e
sage: E.q_eigenform(10)