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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 435120c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 435120.c1 | 435120c1 | \([0, -1, 0, 109399099, -382444272615]\) | \(4807693119590934708224/4879763961468046875\) | \(-146969433677505087180000000\) | \([]\) | \(133539840\) | \(3.7079\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 435120c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 435120c do not have complex multiplication.Modular form 435120.2.a.c
sage: E.q_eigenform(10)