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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 6732c
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6732.b1 | 6732c1 | \([0, 0, 0, -20496, 46094996]\) | \(-5102271397888/4915446963867\) | \(-917340374184715008\) | \([]\) | \(129024\) | \(2.1257\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 6732c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 6732c do not have complex multiplication.Modular form 6732.2.a.c
sage: E.q_eigenform(10)