↑

Properties

Label 477950.z
Number of curves $1$
Conductor $477950$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("z1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 477950.z1 has rank \(1\).

Complex multiplication

The elliptic curves in class 477950.z do not have complex multiplication.

Modular form 477950.2.a.z

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

Elliptic curves in class 477950.z

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
477950.z1 477950z1 \([1, 0, 1, -17354350951, -879956879831702]\) \(-2282033126907134425/647168\) \(-163924523478320000000000\) \([]\) \(543628800\) \(4.2614\) \(\Gamma_0(N)\)-optimal