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SageMath
E = EllipticCurve("ca1")
E.isogeny_class()
Elliptic curves in class 98736ca
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 98736.k1 | 98736ca1 | \([0, -1, 0, -209854, -21285845]\) | \(297999868672/115008417\) | \(394449209179222032\) | \([]\) | \(1013760\) | \(2.0754\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 98736ca1 has rank \(1\).
Complex multiplication
The elliptic curves in class 98736ca do not have complex multiplication.Modular form 98736.2.a.ca
sage: E.q_eigenform(10)