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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 7728.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
7728.r1 | 7728t1 | \([0, 1, 0, -253, -7705]\) | \(-7023616000/93934323\) | \(-24047186688\) | \([]\) | \(7200\) | \(0.67356\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 7728.r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 7728.r do not have complex multiplication.Modular form 7728.2.a.r
sage: E.q_eigenform(10)