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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 68800r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
68800.p1 | 68800r1 | \([0, 1, 0, -33, -31937]\) | \(-2/215\) | \(-440320000000\) | \([]\) | \(86016\) | \(0.91312\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 68800r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 68800r do not have complex multiplication.Modular form 68800.2.a.r
sage: E.q_eigenform(10)