Properties

Label 14586i
Number of curves $1$
Conductor $14586$
CM no
Rank $1$

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Show commands: SageMath
sage: E = EllipticCurve("i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 14586i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14586.l1 14586i1 \([1, 1, 1, 225, 1059]\) \(1259362112399/1131450606\) \(-1131450606\) \([]\) \(7296\) \(0.42461\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 14586i1 has rank \(1\).

Complex multiplication

The elliptic curves in class 14586i do not have complex multiplication.

Modular form 14586.2.a.i

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + 3q^{7} + q^{8} + q^{9} + q^{10} - q^{11} - q^{12} - q^{13} + 3q^{14} - q^{15} + q^{16} + q^{17} + q^{18} - 4q^{19} + O(q^{20})\)  Toggle raw display