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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 33810r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
33810.s1 | 33810r1 | \([1, 1, 0, -443342, 108734004]\) | \(196673474890182710329/9225032263925760\) | \(452026580932362240\) | \([]\) | \(514080\) | \(2.1486\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 33810r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 33810r do not have complex multiplication.Modular form 33810.2.a.r
sage: E.q_eigenform(10)