Properties

Label 43758.n
Number of curves $4$
Conductor $43758$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 43758.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43758.n1 43758t3 \([1, -1, 1, -29656985, 62160880889]\) \(3957101249824708884951625/772310238681366528\) \(563014163998716198912\) \([6]\) \(3649536\) \(2.9814\)  
43758.n2 43758t4 \([1, -1, 1, -26523545, 75806385401]\) \(-2830680648734534916567625/1766676274677722124288\) \(-1287907004240059428605952\) \([6]\) \(7299072\) \(3.3279\)  
43758.n3 43758t1 \([1, -1, 1, -902930, -213616879]\) \(111675519439697265625/37528570137307392\) \(27358327630097088768\) \([2]\) \(1216512\) \(2.4321\) \(\Gamma_0(N)\)-optimal
43758.n4 43758t2 \([1, -1, 1, 2634430, -1478576815]\) \(2773679829880629422375/2899504554614368272\) \(-2113738820313874470288\) \([2]\) \(2433024\) \(2.7786\)  

Rank

sage: E.rank()
 

The elliptic curves in class 43758.n have rank \(0\).

Complex multiplication

The elliptic curves in class 43758.n do not have complex multiplication.

Modular form 43758.2.a.n

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - 4 q^{7} + q^{8} - q^{11} + q^{13} - 4 q^{14} + q^{16} - q^{17} + 2 q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.