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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 198744.dd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 198744.dd1 | 198744v1 | \([0, 1, 0, 328480, -163610784]\) | \(68782/243\) | \(-13847796088938878976\) | \([]\) | \(3628800\) | \(2.3559\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 198744.dd1 has rank \(1\).
Complex multiplication
The elliptic curves in class 198744.dd do not have complex multiplication.Modular form 198744.2.a.dd
sage: E.q_eigenform(10)