Properties

Label 7350g
Number of curves $6$
Conductor $7350$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("7350.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7350g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7350.p6 7350g1 [1, 1, 0, 12225, 733125] [2] 36864 \(\Gamma_0(N)\)-optimal
7350.p5 7350g2 [1, 1, 0, -85775, 7495125] [2, 2] 73728  
7350.p4 7350g3 [1, 1, 0, -453275, -111207375] [2] 147456  
7350.p2 7350g4 [1, 1, 0, -1286275, 560925625] [2, 2] 147456  
7350.p1 7350g5 [1, 1, 0, -20580025, 35926369375] [2] 294912  
7350.p3 7350g6 [1, 1, 0, -1200525, 639043875] [2] 294912  

Rank

sage: E.rank()
 

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

Modular form 7350.2.a.p

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} + q^{6} - q^{8} + q^{9} + 4q^{11} - q^{12} - 2q^{13} + q^{16} + 2q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.