Properties

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

Related objects

Downloads

Learn more

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

Elliptic curves in class 14586a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
14586.b1 14586a1 \([1, 1, 0, -362681, 88298661]\) \(-5275941807135921123097/326485867713527808\) \(-326485867713527808\) \([]\) \(234080\) \(2.1149\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 14586a1 has rank \(1\).

Complex multiplication

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

Modular form 14586.2.a.a

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