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SageMath
E = EllipticCurve("g1")
E.isogeny_class()
Elliptic curves in class 10005.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
10005.g1 | 10005m1 | \([0, 1, 1, -104207741, 135268278965]\) | \(125147927114815865709295304704/64514985611316331088611125\) | \(64514985611316331088611125\) | \([]\) | \(2140320\) | \(3.6445\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 10005.g1 has rank \(1\).
Complex multiplication
The elliptic curves in class 10005.g do not have complex multiplication.Modular form 10005.2.a.g
sage: E.q_eigenform(10)