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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 198198c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 198198.cw1 | 198198c1 | \([1, -1, 1, -109427099, -443083848501]\) | \(-112205650221491190337/745029571313664\) | \(-962181827309398308028416\) | \([]\) | \(54454400\) | \(3.4375\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 198198c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 198198c do not have complex multiplication.Modular form 198198.2.a.c
sage: E.q_eigenform(10)