Properties

Label 4641.f
Number of curves $1$
Conductor $4641$
CM no
Rank $1$

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

Elliptic curves in class 4641.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4641.f1 4641c1 \([0, -1, 1, -22750, 1919349]\) \(-1302227927110660096/825290486657091\) \(-825290486657091\) \([]\) \(32736\) \(1.5637\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4641.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 4641.f do not have complex multiplication.

Modular form 4641.2.a.f

sage: E.q_eigenform(10)
 
\(q + 2q^{2} - q^{3} + 2q^{4} + q^{5} - 2q^{6} - q^{7} + q^{9} + 2q^{10} + 2q^{11} - 2q^{12} + q^{13} - 2q^{14} - q^{15} - 4q^{16} + q^{17} + 2q^{18} - 7q^{19} + O(q^{20})\)  Toggle raw display