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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 18207c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 18207.d1 | 18207c1 | \([1, -1, 0, -30399, 359954]\) | \(610929/343\) | \(1744267220849727\) | \([]\) | \(102816\) | \(1.6147\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 18207c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 18207c do not have complex multiplication.Modular form 18207.2.a.c
sage: E.q_eigenform(10)