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SageMath
E = EllipticCurve("k1")
E.isogeny_class()
Elliptic curves in class 209484.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
209484.k1 | 209484g1 | \([0, 0, 0, -2067861, 106065029]\) | \(299591084078848/171885556953\) | \(561045703335270093072\) | \([]\) | \(6815232\) | \(2.6710\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 209484.k1 has rank \(0\).
Complex multiplication
The elliptic curves in class 209484.k do not have complex multiplication.Modular form 209484.2.a.k
sage: E.q_eigenform(10)