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SageMath
E = EllipticCurve("ct1")
E.isogeny_class()
Elliptic curves in class 164730ct
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 164730.x1 | 164730ct1 | \([1, 1, 0, 5018, 38164]\) | \(48337323922871/29918160000\) | \(-8646348240000\) | \([]\) | \(435456\) | \(1.1715\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 164730ct1 has rank \(1\).
Complex multiplication
The elliptic curves in class 164730ct do not have complex multiplication.Modular form 164730.2.a.ct
sage: E.q_eigenform(10)