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SageMath
E = EllipticCurve("e1")
E.isogeny_class()
Elliptic curves in class 101400e
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 101400.s1 | 101400e1 | \([0, -1, 0, 41061367, 66631046637]\) | \(396555344454656/328867205355\) | \(-6349516746449448780000000\) | \([]\) | \(21288960\) | \(3.4469\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 101400e1 has rank \(1\).
Complex multiplication
The elliptic curves in class 101400e do not have complex multiplication.Modular form 101400.2.a.e
sage: E.q_eigenform(10)