Properties

Label 44100.q
Number of curves $2$
Conductor $44100$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 44100.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44100.q1 44100ce2 \([0, 0, 0, -8878800, -10183155500]\) \(-225637236736/1715\) \(-588355590060000000\) \([]\) \(1244160\) \(2.5845\)  
44100.q2 44100ce1 \([0, 0, 0, -58800, -26925500]\) \(-65536/875\) \(-300181423500000000\) \([]\) \(414720\) \(2.0352\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 44100.q have rank \(0\).

Complex multiplication

The elliptic curves in class 44100.q do not have complex multiplication.

Modular form 44100.2.a.q

sage: E.q_eigenform(10)
 
\(q - 3 q^{11} - q^{13} + 3 q^{17} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.