Properties

Label 37440fv
Number of curves $2$
Conductor $37440$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("fv1")
 
E.isogeny_class()
 

Elliptic curves in class 37440fv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37440.dq2 37440fv1 \([0, 0, 0, 25908, -1697776]\) \(40254822716/49359375\) \(-2358180864000000\) \([2]\) \(122880\) \(1.6358\) \(\Gamma_0(N)\)-optimal
37440.dq1 37440fv2 \([0, 0, 0, -154092, -16313776]\) \(4234737878642/1247410125\) \(119191893590016000\) \([2]\) \(245760\) \(1.9824\)  

Rank

sage: E.rank()
 

The elliptic curves in class 37440fv have rank \(1\).

Complex multiplication

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

Modular form 37440.2.a.fv

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.