Properties

Label 4400m
Number of curves 3
Conductor 4400
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("4400.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 4400m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
4400.i3 4400m1 [0, -1, 0, -133, -1363] [] 1120 \(\Gamma_0(N)\)-optimal
4400.i2 4400m2 [0, -1, 0, -4133, 186637] [] 5600  
4400.i1 4400m3 [0, -1, 0, -3128133, 2130534637] [] 28000  

Rank

sage: E.rank()
 

The elliptic curves in class 4400m have rank \(0\).

Modular form 4400.2.a.i

sage: E.q_eigenform(10)
 
\( q - q^{3} - 2q^{7} - 2q^{9} - q^{11} - 4q^{13} + 2q^{17} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.