↑

Properties

Label 422142.f
Number of curves $1$
Conductor $422142$
CM no
Rank $1$

Related objects

Downloads

Learn more

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

Rank

Copy content sage:E.rank()
 

The elliptic curve 422142.f1 has rank \(1\).

Complex multiplication

The elliptic curves in class 422142.f do not have complex multiplication.

Modular form 422142.2.a.f

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

Elliptic curves in class 422142.f

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
422142.f1 422142f1 \([1, 1, 0, -2262808, -1311149006]\) \(-16362303361609/864234\) \(-67679016053339754\) \([]\) \(8266752\) \(2.2975\) \(\Gamma_0(N)\)-optimal