Properties

Label 7350.cj
Number of curves $2$
Conductor $7350$
CM no
Rank $0$
Graph

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

Elliptic curves in class 7350.cj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
7350.cj1 7350cq2 \([1, 0, 0, -168463, -25898083]\) \(838561807/26244\) \(16547500970437500\) \([2]\) \(71680\) \(1.8872\)  
7350.cj2 7350cq1 \([1, 0, 0, 3037, -1373583]\) \(4913/1296\) \(-817160541750000\) \([2]\) \(35840\) \(1.5406\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 7350.cj have rank \(0\).

Complex multiplication

The elliptic curves in class 7350.cj do not have complex multiplication.

Modular form 7350.2.a.cj

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} - 4 q^{11} + q^{12} - 4 q^{13} + q^{16} + q^{18} + 4 q^{19} + O(q^{20})\) 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 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.