Properties

Label 53130b
Number of curves $1$
Conductor $53130$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("b1")
 
E.isogeny_class()
 

Elliptic curves in class 53130b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
53130.b1 53130b1 \([1, 1, 0, 25581252, 58642887888]\) \(1851352314787299899532057911/2556487378990533244354560\) \(-2556487378990533244354560\) \([]\) \(13844160\) \(3.3691\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 53130b1 has rank \(1\).

Complex multiplication

The elliptic curves in class 53130b do not have complex multiplication.

Modular form 53130.2.a.b

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