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Properties

Label 184110be
Number of curves $4$
Conductor $184110$
CM no
Rank $2$
Graph

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Show commands: SageMath
E = EllipticCurve("be1")
 
E.isogeny_class()
 

Elliptic curves in class 184110be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
184110.p3 184110be1 \([1, 0, 1, -36469, -2343808]\) \(114013572049/15667200\) \(737077226803200\) \([2]\) \(1327104\) \(1.5796\) \(\Gamma_0(N)\)-optimal
184110.p2 184110be2 \([1, 0, 1, -151989, 20436736]\) \(8253429989329/936360000\) \(44051881133160000\) \([2, 2]\) \(2654208\) \(1.9262\)  
184110.p1 184110be3 \([1, 0, 1, -2361309, 1396401232]\) \(30949975477232209/478125000\) \(22493811853125000\) \([2]\) \(5308416\) \(2.2728\)  
184110.p4 184110be4 \([1, 0, 1, 209011, 102889136]\) \(21464092074671/109596256200\) \(-5156052427230712200\) \([2]\) \(5308416\) \(2.2728\)  

Rank

sage: E.rank()
 

The elliptic curves in class 184110be have rank \(2\).

Complex multiplication

The elliptic curves in class 184110be do not have complex multiplication.

Modular form 184110.2.a.be

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - 4 q^{7} - q^{8} + q^{9} + q^{10} - 4 q^{11} + q^{12} + 2 q^{13} + 4 q^{14} - q^{15} + q^{16} + q^{17} - q^{18} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.