Properties

Label 157170.j
Number of curves $1$
Conductor $157170$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 157170.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
157170.j1 157170cy1 \([1, 1, 0, -3895622, 2973232956]\) \(-1354547383894636849/8173828125000\) \(-39453507158203125000\) \([]\) \(8985600\) \(2.5997\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 157170.j1 has rank \(1\).

Complex multiplication

The elliptic curves in class 157170.j do not have complex multiplication.

Modular form 157170.2.a.j

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