Properties

Label 185130.by
Number of curves $1$
Conductor $185130$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("by1")
 
E.isogeny_class()
 

Elliptic curves in class 185130.by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
185130.by1 185130ev1 \([1, -1, 0, -123624, -29738032]\) \(-4368317413923/5475734000\) \(-261916113620898000\) \([]\) \(2304000\) \(2.0356\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 185130.by1 has rank \(1\).

Complex multiplication

The elliptic curves in class 185130.by do not have complex multiplication.

Modular form 185130.2.a.by

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