Properties

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

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 12138.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12138.l1 12138k1 \([1, 0, 1, -10844, -450142]\) \(-5841725401/231336\) \(-5583888662184\) \([]\) \(34560\) \(1.2145\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12138.l1 has rank \(1\).

Complex multiplication

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

Modular form 12138.2.a.l

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