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SageMath
E = EllipticCurve("fp1")
E.isogeny_class()
Elliptic curves in class 123840fp
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 123840.p1 | 123840fp1 | \([0, 0, 0, -2493228, -1524426352]\) | \(-71751706663500872/503130234375\) | \(-12018710638080000000\) | \([]\) | \(3268608\) | \(2.4944\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 123840fp1 has rank \(0\).
Complex multiplication
The elliptic curves in class 123840fp do not have complex multiplication.Modular form 123840.2.a.fp
sage: E.q_eigenform(10)