↑

Properties

Label 459186m
Number of curves $1$
Conductor $459186$
CM no
Rank $2$

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("m1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 459186m1 has rank \(2\).

Complex multiplication

The elliptic curves in class 459186m do not have complex multiplication.

Modular form 459186.2.a.m

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

Elliptic curves in class 459186m

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
459186.m1 459186m1 \([1, 1, 0, 18406428, 15775847568]\) \(820042249883887706995199/602279099584202529216\) \(-506516722750314327070656\) \([]\) \(69189120\) \(3.2368\) \(\Gamma_0(N)\)-optimal