Properties

Label 37440.eq
Number of curves $6$
Conductor $37440$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("eq1")
 
E.isogeny_class()
 

Elliptic curves in class 37440.eq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
37440.eq1 37440cb6 \([0, 0, 0, -5192652, 4554407536]\) \(81025909800741361/11088090\) \(2118966997155840\) \([2]\) \(786432\) \(2.3531\)  
37440.eq2 37440cb4 \([0, 0, 0, -486732, -130599056]\) \(66730743078481/60937500\) \(11645337600000000\) \([2]\) \(393216\) \(2.0065\)  
37440.eq3 37440cb3 \([0, 0, 0, -325452, 70742896]\) \(19948814692561/231344100\) \(44210545990041600\) \([2, 2]\) \(393216\) \(2.0065\)  
37440.eq4 37440cb5 \([0, 0, 0, -66252, 180332656]\) \(-168288035761/73415764890\) \(-14029971155795312640\) \([2]\) \(786432\) \(2.3531\)  
37440.eq5 37440cb2 \([0, 0, 0, -37452, -1026704]\) \(30400540561/15210000\) \(2906676264960000\) \([2, 2]\) \(196608\) \(1.6600\)  
37440.eq6 37440cb1 \([0, 0, 0, 8628, -123536]\) \(371694959/249600\) \(-47699302809600\) \([2]\) \(98304\) \(1.3134\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 37440.2.a.eq

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

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.