Properties

Label 7350.cc
Number of curves $4$
Conductor $7350$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("7350.cc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7350.cc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7350.cc1 7350cc4 [1, 1, 1, -40573, -3152269] [2] 28800  
7350.cc2 7350cc2 [1, 1, 1, -2598, 49881] [2] 5760  
7350.cc3 7350cc3 [1, 1, 1, -1373, -94669] [2] 14400  
7350.cc4 7350cc1 [1, 1, 1, -148, 881] [2] 2880 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 7350.2.a.cc

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} - q^{6} + q^{8} + q^{9} + 2q^{11} - q^{12} + 6q^{13} + q^{16} + 2q^{17} + q^{18} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.