Properties

Label 18032.l
Number of curves $4$
Conductor $18032$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 18032.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
18032.l1 18032x3 \([0, 0, 0, -96971, 11620154]\) \(209267191953/55223\) \(26611428257792\) \([2]\) \(61440\) \(1.5605\)  
18032.l2 18032x2 \([0, 0, 0, -6811, 133770]\) \(72511713/25921\) \(12491078569984\) \([2, 2]\) \(30720\) \(1.2139\)  
18032.l3 18032x1 \([0, 0, 0, -2891, -58310]\) \(5545233/161\) \(77584338944\) \([2]\) \(15360\) \(0.86732\) \(\Gamma_0(N)\)-optimal
18032.l4 18032x4 \([0, 0, 0, 20629, 940506]\) \(2014698447/1958887\) \(-943968651931648\) \([4]\) \(61440\) \(1.5605\)  

Rank

sage: E.rank()
 

The elliptic curves in class 18032.l have rank \(2\).

Complex multiplication

The elliptic curves in class 18032.l do not have complex multiplication.

Modular form 18032.2.a.l

sage: E.q_eigenform(10)
 
\(q - 2 q^{5} - 3 q^{9} - 4 q^{11} - 6 q^{13} + 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.