Properties

Label 7350.bd
Number of curves $8$
Conductor $7350$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("7350.bd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7350.bd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7350.bd1 7350w7 [1, 0, 1, -7902501, -5380124102] [2] 663552  
7350.bd2 7350w4 [1, 0, 1, -7057251, -7216668602] [2] 221184  
7350.bd3 7350w6 [1, 0, 1, -3308751, 2254688398] [2, 2] 331776  
7350.bd4 7350w3 [1, 0, 1, -3284251, 2290605398] [2] 165888  
7350.bd5 7350w2 [1, 0, 1, -442251, -112158602] [2, 2] 110592  
7350.bd6 7350w5 [1, 0, 1, -99251, -281600602] [2] 221184  
7350.bd7 7350w1 [1, 0, 1, -50251, 1521398] [2] 55296 \(\Gamma_0(N)\)-optimal
7350.bd8 7350w8 [1, 0, 1, 892999, 7590910898] [2] 663552  

Rank

sage: E.rank()
 

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

Modular form 7350.2.a.bd

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

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.