Properties

Label 4410.z
Number of curves 8
Conductor 4410
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("4410.z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4410.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4410.z1 4410bb7 [1, -1, 1, -2352083, -1387851573] [2] 55296  
4410.z2 4410bb8 [1, -1, 1, -200003, -4635669] [2] 55296  
4410.z3 4410bb6 [1, -1, 1, -147083, -21633573] [2, 2] 27648  
4410.z4 4410bb5 [1, -1, 1, -127238, 17500767] [2] 18432  
4410.z5 4410bb4 [1, -1, 1, -30218, -1733889] [2] 18432  
4410.z6 4410bb2 [1, -1, 1, -8168, 259431] [2, 2] 9216  
4410.z7 4410bb3 [1, -1, 1, -5963, -578469] [2] 13824  
4410.z8 4410bb1 [1, -1, 1, 652, 19527] [2] 4608 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 4410.z have rank \(0\).

Modular form 4410.2.a.z

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} - q^{5} + q^{8} - q^{10} - 2q^{13} + q^{16} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.