Properties

Label 36414.l
Number of curves $4$
Conductor $36414$
CM no
Rank $1$
Graph

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

Elliptic curves in class 36414.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
36414.l1 36414bh4 \([1, -1, 0, -13210533, -18477825219]\) \(14489843500598257/6246072\) \(109907680537767672\) \([2]\) \(1769472\) \(2.6125\)  
36414.l2 36414bh3 \([1, -1, 0, -1766133, 477971469]\) \(34623662831857/14438442312\) \(254062986320087835912\) \([2]\) \(1769472\) \(2.6125\)  
36414.l3 36414bh2 \([1, -1, 0, -829773, -285536475]\) \(3590714269297/73410624\) \(1291754467554997824\) \([2, 2]\) \(884736\) \(2.2659\)  
36414.l4 36414bh1 \([1, -1, 0, 2547, -13367835]\) \(103823/4386816\) \(-77191676866031616\) \([2]\) \(442368\) \(1.9193\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 36414.l have rank \(1\).

Complex multiplication

The elliptic curves in class 36414.l do not have complex multiplication.

Modular form 36414.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{4} - 2q^{5} + q^{7} - q^{8} + 2q^{10} - 6q^{13} - q^{14} + q^{16} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.