Properties

Label 37440cq
Number of curves $2$
Conductor $37440$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cq1")
 
E.isogeny_class()
 

Elliptic curves in class 37440cq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37440.fi2 37440cq1 \([0, 0, 0, 25908, 1697776]\) \(40254822716/49359375\) \(-2358180864000000\) \([2]\) \(122880\) \(1.6358\) \(\Gamma_0(N)\)-optimal
37440.fi1 37440cq2 \([0, 0, 0, -154092, 16313776]\) \(4234737878642/1247410125\) \(119191893590016000\) \([2]\) \(245760\) \(1.9824\)  

Rank

sage: E.rank()
 

The elliptic curves in class 37440cq have rank \(0\).

Complex multiplication

The elliptic curves in class 37440cq do not have complex multiplication.

Modular form 37440.2.a.cq

sage: E.q_eigenform(10)
 
\(q + q^{5} + 2 q^{7} + 4 q^{11} + q^{13} - 2 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.