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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 4998.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4998.r1 | 4998p1 | \([1, 0, 1, -11884, -1502980]\) | \(-4599141247/21489462\) | \(-867177304189434\) | \([]\) | \(28224\) | \(1.5510\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4998.r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4998.r do not have complex multiplication.Modular form 4998.2.a.r
sage: E.q_eigenform(10)