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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 4998.e
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4998.e1 | 4998b1 | \([1, 1, 0, -327492, -72248112]\) | \(1617840527930521321/623760113664\) | \(1497648032907264\) | \([]\) | \(40320\) | \(1.8774\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4998.e1 has rank \(0\).
Complex multiplication
The elliptic curves in class 4998.e do not have complex multiplication.Modular form 4998.2.a.e
sage: E.q_eigenform(10)