Properties

Label 1170.n
Number of curves $4$
Conductor $1170$
CM no
Rank $0$
Graph

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

Elliptic curves in class 1170.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1170.n1 1170n3 \([1, -1, 1, -778757, -264320611]\) \(71647584155243142409/10140000\) \(7392060000\) \([2]\) \(10240\) \(1.7466\)  
1170.n2 1170n4 \([1, -1, 1, -55877, -2815459]\) \(26465989780414729/10571870144160\) \(7706893335092640\) \([2]\) \(10240\) \(1.7466\)  
1170.n3 1170n2 \([1, -1, 1, -48677, -4120099]\) \(17496824387403529/6580454400\) \(4797151257600\) \([2, 2]\) \(5120\) \(1.4000\)  
1170.n4 1170n1 \([1, -1, 1, -2597, -83491]\) \(-2656166199049/2658140160\) \(-1937784176640\) \([4]\) \(2560\) \(1.0534\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1170.n have rank \(0\).

Complex multiplication

The elliptic curves in class 1170.n do not have complex multiplication.

Modular form 1170.2.a.n

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + 4 q^{7} + q^{8} + q^{10} - q^{13} + 4 q^{14} + q^{16} + 2 q^{17} + 4 q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.