Properties

Label 7350bc
Number of curves 8
Conductor 7350
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("7350.w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7350bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7350.w7 7350bc1 [1, 0, 1, 257224, -37815802] [2] 147456 \(\Gamma_0(N)\)-optimal
7350.w6 7350bc2 [1, 0, 1, -1310776, -338871802] [2, 2] 294912  
7350.w4 7350bc3 [1, 0, 1, -18460776, -30522871802] [2] 589824  
7350.w5 7350bc4 [1, 0, 1, -9248776, 10583816198] [2, 2] 589824  
7350.w2 7350bc5 [1, 0, 1, -147061276, 686416316198] [2, 2] 1179648  
7350.w8 7350bc6 [1, 0, 1, 1555724, 33835100198] [2] 1179648  
7350.w1 7350bc7 [1, 0, 1, -2352980026, 43931247491198] [2] 2359296  
7350.w3 7350bc8 [1, 0, 1, -146142526, 695416391198] [2] 2359296  

Rank

sage: E.rank()
 

The elliptic curves in class 7350bc have rank \(1\).

Modular form 7350.2.a.w

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 8 & 8 & 16 & 16 \\ 4 & 2 & 4 & 1 & 2 & 2 & 4 & 4 \\ 8 & 4 & 8 & 2 & 1 & 4 & 2 & 2 \\ 8 & 4 & 8 & 2 & 4 & 1 & 8 & 8 \\ 16 & 8 & 16 & 4 & 2 & 8 & 1 & 4 \\ 16 & 8 & 16 & 4 & 2 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.