Properties

Label 12138.q
Number of curves $1$
Conductor $12138$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 12138.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12138.q1 12138s1 \([1, 1, 1, 283, 2315]\) \(30004847/42336\) \(-3535945056\) \([]\) \(8640\) \(0.51779\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12138.q1 has rank \(1\).

Complex multiplication

The elliptic curves in class 12138.q do not have complex multiplication.

Modular form 12138.2.a.q

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