Properties

Label 37440.da
Number of curves $4$
Conductor $37440$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("da1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 37440.da

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37440.da1 37440fl4 \([0, 0, 0, -299532, 63097616]\) \(31103978031362/195\) \(18632540160\) \([2]\) \(196608\) \(1.5763\)  
37440.da2 37440fl3 \([0, 0, 0, -25932, 158096]\) \(20183398562/11567205\) \(1105263649751040\) \([2]\) \(196608\) \(1.5763\)  
37440.da3 37440fl2 \([0, 0, 0, -18732, 984656]\) \(15214885924/38025\) \(1816672665600\) \([2, 2]\) \(98304\) \(1.2297\)  
37440.da4 37440fl1 \([0, 0, 0, -732, 27056]\) \(-3631696/24375\) \(-291133440000\) \([2]\) \(49152\) \(0.88311\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 37440.2.a.da

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