Properties

Label 12138.u
Number of curves $1$
Conductor $12138$
CM no
Rank $0$

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Show commands for: SageMath
sage: E = EllipticCurve("u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 12138.u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12138.u1 12138u1 \([1, 1, 1, 523951, 62603183]\) \(2280364702703/1560674304\) \(-10886885389105496064\) \([]\) \(416160\) \(2.3415\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 12138.u1 has rank \(0\).

Complex multiplication

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

Modular form 12138.2.a.u

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