Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("4410.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4410r

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4410.t7 4410r1 [1, -1, 0, 92601, 8149693] [2] 49152 \(\Gamma_0(N)\)-optimal
4410.t6 4410r2 [1, -1, 0, -471879, 73290685] [2, 2] 98304  
4410.t5 4410r3 [1, -1, 0, -3329559, -2285438387] [2, 2] 196608  
4410.t4 4410r4 [1, -1, 0, -6645879, 6594269485] [2] 196608  
4410.t2 4410r5 [1, -1, 0, -52942059, -148255335887] [2, 2] 393216  
4410.t8 4410r6 [1, -1, 0, 560061, -7308493655] [2] 393216  
4410.t1 4410r7 [1, -1, 0, -847072809, -9488980043537] [2] 786432  
4410.t3 4410r8 [1, -1, 0, -52611309, -150199418237] [2] 786432  

Rank

sage: E.rank()
 

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

Modular form 4410.2.a.t

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} + 4q^{11} + 2q^{13} + q^{16} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.