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SageMath
E = EllipticCurve("hc1")
E.isogeny_class()
Elliptic curves in class 139650hc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
139650.eh1 | 139650hc1 | \([1, 0, 1, -1660146, -823460732]\) | \(-172041783999846385/1179967488\) | \(-3470549874892800\) | \([]\) | \(2515968\) | \(2.1626\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 139650hc1 has rank \(0\).
Complex multiplication
The elliptic curves in class 139650hc do not have complex multiplication.Modular form 139650.2.a.hc
sage: E.q_eigenform(10)