Properties

Label 34650.cl
Number of curves $4$
Conductor $34650$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 34650.cl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
34650.cl1 34650dx4 \([1, -1, 1, -1497325055, -22299890030553]\) \(260744057755293612689909/8504954620259328\) \(12109593590173926000000000\) \([2]\) \(15360000\) \(3.9070\)  
34650.cl2 34650dx3 \([1, -1, 1, -97645055, -316515950553]\) \(72313087342699809269/11447096545640448\) \(16298698011273216000000000\) \([2]\) \(7680000\) \(3.5605\)  
34650.cl3 34650dx2 \([1, -1, 1, -26494430, 52016015697]\) \(1444540994277943589/15251205665388\) \(21715095566538773437500\) \([2]\) \(3072000\) \(3.1023\)  
34650.cl4 34650dx1 \([1, -1, 1, -26426930, 52296545697]\) \(1433528304665250149/162339408\) \(231143414906250000\) \([2]\) \(1536000\) \(2.7557\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 34650.cl have rank \(0\).

Complex multiplication

The elliptic curves in class 34650.cl do not have complex multiplication.

Modular form 34650.2.a.cl

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

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.