Properties

Label 4400t
Number of curves 4
Conductor 4400
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("4400.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4400t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4400.e4 4400t1 [0, 1, 0, -1133, -14762] [2] 3456 \(\Gamma_0(N)\)-optimal
4400.e3 4400t2 [0, 1, 0, -2508, 26488] [2] 6912  
4400.e2 4400t3 [0, 1, 0, -11133, 442738] [2] 10368  
4400.e1 4400t4 [0, 1, 0, -177508, 28726488] [2] 20736  

Rank

sage: E.rank()
 

The elliptic curves in class 4400t have rank \(1\).

Modular form 4400.2.a.e

sage: E.q_eigenform(10)
 
\( q - 2q^{3} - 4q^{7} + q^{9} + q^{11} + 4q^{13} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.