Properties

Label 24150bl
Number of curves $4$
Conductor $24150$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 24150bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24150.bo3 24150bl1 \([1, 1, 1, -3178088, 2334258281]\) \(-227196402372228188089/19338934824115200\) \(-302170856626800000000\) \([2]\) \(1105920\) \(2.6746\) \(\Gamma_0(N)\)-optimal
24150.bo2 24150bl2 \([1, 1, 1, -51846088, 143666130281]\) \(986396822567235411402169/6336721794060000\) \(99011278032187500000\) \([2]\) \(2211840\) \(3.0212\)  
24150.bo4 24150bl3 \([1, 1, 1, 18841537, 94207781]\) \(47342661265381757089751/27397579603968000000\) \(-428087181312000000000000\) \([2]\) \(3317760\) \(3.2239\)  
24150.bo1 24150bl4 \([1, 1, 1, -75366463, 659455781]\) \(3029968325354577848895529/1753440696000000000000\) \(27397510875000000000000000\) \([2]\) \(6635520\) \(3.5705\)  

Rank

sage: E.rank()
 

The elliptic curves in class 24150bl have rank \(0\).

Complex multiplication

The elliptic curves in class 24150bl do not have complex multiplication.

Modular form 24150.2.a.bl

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} - q^{7} + q^{8} + q^{9} - q^{12} + 4q^{13} - q^{14} + q^{16} + q^{18} + 2q^{19} + O(q^{20})\)  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 Cremona 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 Cremona labels.