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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 100005c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
100005.d1 | 100005c1 | \([0, 1, 1, -249500, 47855441]\) | \(1717659606564845572096/1232397230480685\) | \(1232397230480685\) | \([]\) | \(1539840\) | \(1.8309\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 100005c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 100005c do not have complex multiplication.Modular form 100005.2.a.c
sage: E.q_eigenform(10)