Properties

Label 24150.i
Number of curves $2$
Conductor $24150$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("i1")
 
E.isogeny_class()
 

Elliptic curves in class 24150.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
24150.i1 24150b1 \([1, 1, 0, -1500, -22500]\) \(23912763841/608580\) \(9509062500\) \([2]\) \(23040\) \(0.69719\) \(\Gamma_0(N)\)-optimal
24150.i2 24150b2 \([1, 1, 0, 250, -69750]\) \(109902239/134974350\) \(-2108974218750\) \([2]\) \(46080\) \(1.0438\)  

Rank

sage: E.rank()
 

The elliptic curves in class 24150.i have rank \(1\).

Complex multiplication

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

Modular form 24150.2.a.i

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} - q^{7} - q^{8} + q^{9} + 4 q^{11} - q^{12} - 2 q^{13} + q^{14} + q^{16} - 4 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.