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SageMath
E = EllipticCurve("n1")
E.isogeny_class()
Elliptic curves in class 10005.n
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10005.n1 | 10005c1 | \([0, -1, 1, -16, -3]\) | \(481890304/250125\) | \(250125\) | \([]\) | \(1440\) | \(-0.27224\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 10005.n1 has rank \(1\).
Complex multiplication
The elliptic curves in class 10005.n do not have complex multiplication.Modular form 10005.2.a.n
sage: E.q_eigenform(10)