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Properties

Label 35490.ct
Number of curves $4$
Conductor $35490$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("ct1")
 
E.isogeny_class()
 

Elliptic curves in class 35490.ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
35490.ct1 35490cu4 \([1, 1, 1, -22966005, -42371553645]\) \(277536408914951281369/2063880\) \(9961954558920\) \([2]\) \(1548288\) \(2.5451\)  
35490.ct2 35490cu3 \([1, 1, 1, -1536805, -563630605]\) \(83161039719198169/19757817763320\) \(95367212600352845880\) \([2]\) \(1548288\) \(2.5451\)  
35490.ct3 35490cu2 \([1, 1, 1, -1435405, -662475325]\) \(67762119444423769/5843073600\) \(28203400240142400\) \([2, 2]\) \(774144\) \(2.1986\)  
35490.ct4 35490cu1 \([1, 1, 1, -83405, -11892925]\) \(-13293525831769/4892160000\) \(-23613521917440000\) \([4]\) \(387072\) \(1.8520\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 35490.ct have rank \(0\).

Complex multiplication

The elliptic curves in class 35490.ct do not have complex multiplication.

Modular form 35490.2.a.ct

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{7} + q^{8} + q^{9} + q^{10} - 4 q^{11} - q^{12} + q^{14} - q^{15} + q^{16} + 6 q^{17} + q^{18} - 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.