Properties

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

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Show commands: SageMath
E = EllipticCurve("j1")
 
E.isogeny_class()
 

Elliptic curves in class 24150j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24150.s4 24150j1 \([1, 1, 0, -14975, -1156875]\) \(-23771111713777/22848457968\) \(-357007155750000\) \([2]\) \(122880\) \(1.4886\) \(\Gamma_0(N)\)-optimal
24150.s3 24150j2 \([1, 1, 0, -279475, -56966375]\) \(154502321244119857/55101928644\) \(860967635062500\) \([2, 2]\) \(245760\) \(1.8351\)  
24150.s2 24150j3 \([1, 1, 0, -319725, -39538125]\) \(231331938231569617/90942310746882\) \(1420973605420031250\) \([2]\) \(491520\) \(2.1817\)  
24150.s1 24150j4 \([1, 1, 0, -4471225, -3640912625]\) \(632678989847546725777/80515134\) \(1258048968750\) \([2]\) \(491520\) \(2.1817\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 24150.2.a.j

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