Properties

Label 4410m
Number of curves 4
Conductor 4410
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("4410.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4410m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4410.b4 4410m1 [1, -1, 0, 1020, -20224] [2] 6144 \(\Gamma_0(N)\)-optimal
4410.b3 4410m2 [1, -1, 0, -7800, -212500] [2, 2] 12288  
4410.b1 4410m3 [1, -1, 0, -118050, -15581350] [2] 24576  
4410.b2 4410m4 [1, -1, 0, -38670, 2744846] [2] 24576  

Rank

sage: E.rank()
 

The elliptic curves in class 4410m have rank \(1\).

Modular form 4410.2.a.b

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - 4q^{11} + 6q^{13} + q^{16} + 2q^{17} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.