Properties

Label 7350.f
Number of curves 6
Conductor 7350
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("7350.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7350.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7350.f1 7350i3 [1, 1, 0, -1646425, -813818375] [2] 98304  
7350.f2 7350i5 [1, 1, 0, -1119675, 451177875] [2] 196608  
7350.f3 7350i4 [1, 1, 0, -127425, -6249375] [2, 2] 98304  
7350.f4 7350i2 [1, 1, 0, -102925, -12741875] [2, 2] 49152  
7350.f5 7350i1 [1, 1, 0, -4925, -295875] [2] 24576 \(\Gamma_0(N)\)-optimal
7350.f6 7350i6 [1, 1, 0, 472825, -47666625] [2] 196608  

Rank

sage: E.rank()
 

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

Modular form 7350.2.a.f

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

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.