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SageMath
E = EllipticCurve("hr1")
E.isogeny_class()
Elliptic curves in class 139650hr
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
139650.r1 | 139650hr1 | \([1, 1, 0, -102435, -12665925]\) | \(-23565848363/9234\) | \(-46578150879750\) | \([]\) | \(770560\) | \(1.5874\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 139650hr1 has rank \(0\).
Complex multiplication
The elliptic curves in class 139650hr do not have complex multiplication.Modular form 139650.2.a.hr
sage: E.q_eigenform(10)