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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 400710.c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 400710.c1 | 400710c1 | \([1, 1, 0, -10183539618, 395547460425588]\) | \(-2482552139091094565771049649/46377400459591680000\) | \(-2181865663111295485870080000\) | \([]\) | \(740275200\) | \(4.3704\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 400710.c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 400710.c do not have complex multiplication.Modular form 400710.2.a.c
sage: E.q_eigenform(10)