Properties

Label 116688.h
Number of curves $4$
Conductor $116688$
CM no
Rank $0$
Graph

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

Elliptic curves in class 116688.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116688.h1 116688m3 \([0, -1, 0, -52723528, 147344310256]\) \(3957101249824708884951625/772310238681366528\) \(3163382737638877298688\) \([2]\) \(10948608\) \(3.1252\)  
116688.h2 116688m4 \([0, -1, 0, -47152968, 179689209840]\) \(-2830680648734534916567625/1766676274677722124288\) \(-7236306021079949821083648\) \([2]\) \(21897216\) \(3.4718\)  
116688.h3 116688m1 \([0, -1, 0, -1605208, -506351120]\) \(111675519439697265625/37528570137307392\) \(153717023282411077632\) \([2]\) \(3649536\) \(2.5759\) \(\Gamma_0(N)\)-optimal
116688.h4 116688m2 \([0, -1, 0, 4683432, -3504774672]\) \(2773679829880629422375/2899504554614368272\) \(-11876370655700452442112\) \([2]\) \(7299072\) \(2.9225\)  

Rank

sage: E.rank()
 

The elliptic curves in class 116688.h have rank \(0\).

Complex multiplication

The elliptic curves in class 116688.h do not have complex multiplication.

Modular form 116688.2.a.h

sage: E.q_eigenform(10)
 
\(q - q^{3} + 4 q^{7} + q^{9} - q^{11} + q^{13} + q^{17} - 2 q^{19} + O(q^{20})\)  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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.