Properties

Label 134749.a
Number of curves $1$
Conductor $134749$
CM no
Rank $0$

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

Elliptic curves in class 134749.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
134749.a1 134749a1 \([1, 0, 0, -4464, -121619]\) \(-912673/61\) \(-657532135069\) \([]\) \(210496\) \(1.0196\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 134749.a1 has rank \(0\).

Complex multiplication

The elliptic curves in class 134749.a do not have complex multiplication.

Modular form 134749.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - 2 q^{3} - q^{4} + 3 q^{5} + 2 q^{6} + q^{7} + 3 q^{8} + q^{9} - 3 q^{10} + 5 q^{11} + 2 q^{12} - q^{13} - q^{14} - 6 q^{15} - q^{16} + 4 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display