Properties

Label 44436j
Number of curves $4$
Conductor $44436$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 44436j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
44436.l4 44436j1 \([0, 1, 0, 3527, 28664]\) \(2048000/1323\) \(-3133623698352\) \([2]\) \(71280\) \(1.0867\) \(\Gamma_0(N)\)-optimal
44436.l3 44436j2 \([0, 1, 0, -14988, 221220]\) \(9826000/5103\) \(193389348241152\) \([2]\) \(142560\) \(1.4333\)  
44436.l2 44436j3 \([0, 1, 0, -59953, 5798996]\) \(-10061824000/352947\) \(-835981166638128\) \([2]\) \(213840\) \(1.6360\)  
44436.l1 44436j4 \([0, 1, 0, -967188, 365789844]\) \(2640279346000/3087\) \(116988618071808\) \([2]\) \(427680\) \(1.9826\)  

Rank

sage: E.rank()
 

The elliptic curves in class 44436j have rank \(0\).

Complex multiplication

The elliptic curves in class 44436j do not have complex multiplication.

Modular form 44436.2.a.j

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{7} + q^{9} + 6 q^{11} + 2 q^{13} + 4 q^{19} + O(q^{20})\) 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 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.