Properties

Label 1170h
Number of curves $2$
Conductor $1170$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("h1")
 
E.isogeny_class()
 

Elliptic curves in class 1170h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1170.l2 1170h1 \([1, -1, 1, 151252, -13465169]\) \(19441890357117957/15208161280000\) \(-299342238474240000\) \([2]\) \(15360\) \(2.0414\) \(\Gamma_0(N)\)-optimal
1170.l1 1170h2 \([1, -1, 1, -712748, -115762769]\) \(2034416504287874043/882294347833600\) \(17366199648408748800\) \([2]\) \(30720\) \(2.3879\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 1170.2.a.h

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} + 2 q^{7} + q^{8} - q^{10} + 4 q^{11} - q^{13} + 2 q^{14} + q^{16} - 4 q^{17} + 6 q^{19} + O(q^{20})\) 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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.