Properties

Label 122304.cj
Number of curves $2$
Conductor $122304$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cj1")
 
E.isogeny_class()
 

Elliptic curves in class 122304.cj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
122304.cj1 122304j1 \([0, -1, 0, -653, 3165]\) \(256000/117\) \(14095291392\) \([2]\) \(73728\) \(0.64235\) \(\Gamma_0(N)\)-optimal
122304.cj2 122304j2 \([0, -1, 0, 2287, 21393]\) \(686000/507\) \(-977273536512\) \([2]\) \(147456\) \(0.98893\)  

Rank

sage: E.rank()
 

The elliptic curves in class 122304.cj have rank \(0\).

Complex multiplication

The elliptic curves in class 122304.cj do not have complex multiplication.

Modular form 122304.2.a.cj

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} + 2 q^{11} - q^{13} + 6 q^{17} - 4 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.