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SageMath
E = EllipticCurve("gc1")
E.isogeny_class()
Elliptic curves in class 88200gc
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 88200.fl1 | 88200gc1 | \([0, 0, 0, -1575, -23625]\) | \(48384\) | \(8930250000\) | \([]\) | \(47040\) | \(0.69966\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 88200gc1 has rank \(0\).
Complex multiplication
The elliptic curves in class 88200gc do not have complex multiplication.Modular form 88200.2.a.gc
sage: E.q_eigenform(10)