Properties

Label 137904r
Number of curves $1$
Conductor $137904$
CM no
Rank $0$

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Show commands: SageMath
E = EllipticCurve("r1")
 
E.isogeny_class()
 

Elliptic curves in class 137904r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
137904.cx1 137904r1 \([0, 1, 0, -11717, -1950285]\) \(-53248/459\) \(-1533625962246144\) \([]\) \(786240\) \(1.5965\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 137904r1 has rank \(0\).

Complex multiplication

The elliptic curves in class 137904r do not have complex multiplication.

Modular form 137904.2.a.r

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