Properties

Label 722.f
Number of curves $1$
Conductor $722$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 722.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
722.f1 722d1 \([1, -1, 1, -429, 77485]\) \(-27/8\) \(-2581501582232\) \([]\) \(2280\) \(1.0608\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 722.f1 has rank \(0\).

Complex multiplication

The elliptic curves in class 722.f do not have complex multiplication.

Modular form 722.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{2} + 3 q^{3} + q^{4} + 2 q^{5} + 3 q^{6} - 3 q^{7} + q^{8} + 6 q^{9} + 2 q^{10} - 2 q^{11} + 3 q^{12} - 3 q^{13} - 3 q^{14} + 6 q^{15} + q^{16} - q^{17} + 6 q^{18} + O(q^{20})\) Copy content Toggle raw display