Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1170.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1170.g1 1170g4 \([1, -1, 0, -10764, 410670]\) \(189208196468929/10860320250\) \(7917173462250\) \([6]\) \(2304\) \(1.2291\)  
1170.g2 1170g2 \([1, -1, 0, -1854, -30132]\) \(967068262369/4928040\) \(3592541160\) \([2]\) \(768\) \(0.67982\)  
1170.g3 1170g1 \([1, -1, 0, -54, -972]\) \(-24137569/561600\) \(-409406400\) \([2]\) \(384\) \(0.33325\) \(\Gamma_0(N)\)-optimal
1170.g4 1170g3 \([1, -1, 0, 486, 25920]\) \(17394111071/411937500\) \(-300302437500\) \([6]\) \(1152\) \(0.88256\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1170.2.a.g

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.