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Properties

Label 374790.a
Number of curves $4$
Conductor $374790$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 374790.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
374790.a1 374790a4 \([1, 1, 0, -21837303, -38917630737]\) \(1297629112899490489/14051741136030\) \(12470971982685746726430\) \([2]\) \(49152000\) \(3.0551\)  
374790.a2 374790a2 \([1, 1, 0, -2473153, 519397153]\) \(1884980132364889/959008904100\) \(851123932500525992100\) \([2, 2]\) \(24576000\) \(2.7085\)  
374790.a3 374790a1 \([1, 1, 0, -1992653, 1080909453]\) \(985936447812889/979290000\) \(869123479766490000\) \([2]\) \(12288000\) \(2.3619\) \(\Gamma_0(N)\)-optimal
374790.a4 374790a3 \([1, 1, 0, 9202997, 4029247843]\) \(97127300136968711/64095340372830\) \(-56884850515834537387230\) \([2]\) \(49152000\) \(3.0551\)  

Rank

sage: E.rank()
 

The elliptic curves in class 374790.a have rank \(0\).

Complex multiplication

The elliptic curves in class 374790.a do not have complex multiplication.

Modular form 374790.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 4 q^{7} - q^{8} + q^{9} + q^{10} - 4 q^{11} - q^{12} - q^{13} + 4 q^{14} + q^{15} + q^{16} + 2 q^{17} - q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.