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Properties

Label 43095.n
Number of curves $4$
Conductor $43095$
CM no
Rank $0$
Graph

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

Elliptic curves in class 43095.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
43095.n1 43095f4 \([1, 1, 0, -176777, -28678554]\) \(126574061279329/16286595\) \(78612283325355\) \([2]\) \(301056\) \(1.6874\)  
43095.n2 43095f2 \([1, 1, 0, -12002, -370209]\) \(39616946929/10989225\) \(53042890133025\) \([2, 2]\) \(150528\) \(1.3409\)  
43095.n3 43095f1 \([1, 1, 0, -4397, 105864]\) \(1948441249/89505\) \(432023539545\) \([2]\) \(75264\) \(0.99428\) \(\Gamma_0(N)\)-optimal
43095.n4 43095f3 \([1, 1, 0, 31093, -2378436]\) \(688699320191/910381875\) \(-4394239427686875\) \([2]\) \(301056\) \(1.6874\)  

Rank

sage: E.rank()
 

The elliptic curves in class 43095.n have rank \(0\).

Complex multiplication

The elliptic curves in class 43095.n do not have complex multiplication.

Modular form 43095.2.a.n

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} - q^{4} + q^{5} - q^{6} + 4 q^{7} - 3 q^{8} + q^{9} + q^{10} + 4 q^{11} + q^{12} + 4 q^{14} - q^{15} - q^{16} - q^{17} + q^{18} + 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.