Properties

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

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Show commands: SageMath
sage: E = EllipticCurve("m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 1170.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1170.m1 1170m3 \([1, -1, 1, -4352, 111561]\) \(12501706118329/2570490\) \(1873887210\) \([2]\) \(1024\) \(0.77634\)  
1170.m2 1170m2 \([1, -1, 1, -302, 1401]\) \(4165509529/1368900\) \(997928100\) \([2, 2]\) \(512\) \(0.42977\)  
1170.m3 1170m1 \([1, -1, 1, -122, -471]\) \(273359449/9360\) \(6823440\) \([2]\) \(256\) \(0.083192\) \(\Gamma_0(N)\)-optimal
1170.m4 1170m4 \([1, -1, 1, 868, 8889]\) \(99317171591/106616250\) \(-77723246250\) \([2]\) \(1024\) \(0.77634\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1170.2.a.m

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + q^{8} + q^{10} - q^{13} + q^{16} + 6q^{17} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.