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SageMath
E = EllipticCurve("i1")
E.isogeny_class()
Elliptic curves in class 4400i
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4400.j1 | 4400i1 | \([0, -1, 0, 32, 32]\) | \(13718/11\) | \(-2816000\) | \([]\) | \(384\) | \(-0.074549\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4400i1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4400i do not have complex multiplication.Modular form 4400.2.a.i
sage: E.q_eigenform(10)