Properties

Label 135501a
Number of curves $1$
Conductor $135501$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 135501a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
135501.a1 135501a1 \([0, -1, 1, -11852, -184450]\) \(207474688/102789\) \(91225615866309\) \([]\) \(856800\) \(1.3717\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 135501a1 has rank \(1\).

Complex multiplication

The elliptic curves in class 135501a do not have complex multiplication.

Modular form 135501.2.a.a

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