Properties

Label 3630w
Number of curves 8
Conductor 3630
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("3630.w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3630w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3630.w8 3630w1 [1, 0, 0, 179, -2815] [2] 2880 \(\Gamma_0(N)\)-optimal
3630.w6 3630w2 [1, 0, 0, -2241, -37179] [2, 2] 5760  
3630.w7 3630w3 [1, 0, 0, -1636, 83216] [2] 8640  
3630.w4 3630w4 [1, 0, 0, -34911, -2513565] [2] 11520  
3630.w5 3630w5 [1, 0, 0, -8291, 249591] [2] 11520  
3630.w3 3630w6 [1, 0, 0, -40356, 3111120] [2, 2] 17280  
3630.w2 3630w7 [1, 0, 0, -54876, 668856] [2] 34560  
3630.w1 3630w8 [1, 0, 0, -645356, 199494120] [2] 34560  

Rank

sage: E.rank()
 

The elliptic curves in class 3630w have rank \(0\).

Modular form 3630.2.a.w

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + 4q^{7} + q^{8} + q^{9} - q^{10} + q^{12} - 2q^{13} + 4q^{14} - q^{15} + q^{16} - 6q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.