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SageMath
E = EllipticCurve("dd1")
E.isogeny_class()
Elliptic curves in class 84150.dd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
84150.dd1 | 84150ck1 | \([1, -1, 0, 397683, -14036409]\) | \(610641930681719/360747465210\) | \(-4109139095907656250\) | \([]\) | \(1797120\) | \(2.2610\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 84150.dd1 has rank \(1\).
Complex multiplication
The elliptic curves in class 84150.dd do not have complex multiplication.Modular form 84150.2.a.dd
sage: E.q_eigenform(10)