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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 88200.r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
88200.r1 | 88200cu1 | \([0, 0, 0, -4501875, -1995831250]\) | \(2450\) | \(4118489130420000000000\) | \([]\) | \(4112640\) | \(2.8451\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 88200.r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 88200.r do not have complex multiplication.Modular form 88200.2.a.r
sage: E.q_eigenform(10)