Properties

Label 122694.r
Number of curves $1$
Conductor $122694$
CM no
Rank $0$

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

Elliptic curves in class 122694.r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
122694.r1 122694q1 \([1, 1, 0, -528167, -137736243]\) \(54424690756969/4209228936\) \(1260217084102057224\) \([]\) \(2177280\) \(2.2176\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 122694.r1 has rank \(0\).

Complex multiplication

The elliptic curves in class 122694.r do not have complex multiplication.

Modular form 122694.2.a.r

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