Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4641.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4641.a1 4641f1 \([0, 1, 1, -14, -310]\) \(-325660672/40000779\) \(-40000779\) \([]\) \(2208\) \(0.13816\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 4641.a1 has rank \(1\).

Complex multiplication

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

Modular form 4641.2.a.a

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