Properties

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

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

Elliptic curves in class 37440.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37440.l1 37440bu1 \([0, 0, 0, -2928, -5848]\) \(3718856704/2132325\) \(1591772083200\) \([2]\) \(49152\) \(1.0310\) \(\Gamma_0(N)\)-optimal
37440.l2 37440bu2 \([0, 0, 0, 11652, -46672]\) \(14647977776/8555625\) \(-102187837440000\) \([2]\) \(98304\) \(1.3776\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 37440.2.a.l

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