Properties

Label 37440.m
Number of curves $2$
Conductor $37440$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 37440.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37440.m1 37440em2 \([0, 0, 0, -26508, -1488112]\) \(10779215329/1232010\) \(235440777461760\) \([2]\) \(147456\) \(1.4900\)  
37440.m2 37440em1 \([0, 0, 0, 2292, -117232]\) \(6967871/35100\) \(-6707714457600\) \([2]\) \(73728\) \(1.1434\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 37440.m have rank \(2\).

Complex multiplication

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

Modular form 37440.2.a.m

sage: E.q_eigenform(10)
 
\(q - q^{5} - 2q^{7} - 4q^{11} + q^{13} - 8q^{17} - 6q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.