Properties

Label 12342r
Number of curves $2$
Conductor $12342$
CM no
Rank $0$
Graph

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

Elliptic curves in class 12342r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
12342.s1 12342r1 [1, 0, 1, -23719, 1403114] [2] 46080 \(\Gamma_0(N)\)-optimal
12342.s2 12342r2 [1, 0, 1, -18879, 1993594] [2] 92160  

Rank

sage: E.rank()
 

The elliptic curves in class 12342r have rank \(0\).

Complex multiplication

The elliptic curves in class 12342r do not have complex multiplication.

Modular form 12342.2.a.r

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

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.