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Properties

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

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Show commands: SageMath
E = EllipticCurve("y1")
 
E.isogeny_class()
 

Elliptic curves in class 12342y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
12342.t1 12342y1 \([1, 1, 1, -305, -1429]\) \(1771561/612\) \(1084195332\) \([2]\) \(11520\) \(0.43542\) \(\Gamma_0(N)\)-optimal
12342.t2 12342y2 \([1, 1, 1, 905, -8689]\) \(46268279/46818\) \(-82940942898\) \([2]\) \(23040\) \(0.78199\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 12342.2.a.y

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

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.