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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 10005.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10005.j1 | 10005n1 | \([0, 1, 1, -1305, 12506]\) | \(245973316796416/69995230125\) | \(69995230125\) | \([]\) | \(6720\) | \(0.78766\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 10005.j1 has rank \(0\).
Complex multiplication
The elliptic curves in class 10005.j do not have complex multiplication.Modular form 10005.2.a.j
sage: E.q_eigenform(10)