Properties

Label 248430iz
Number of curves $4$
Conductor $248430$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("iz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 248430iz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
248430.iz3 248430iz1 [1, 0, 0, -29156, 1207296] [2] 1769472 \(\Gamma_0(N)\)-optimal
248430.iz2 248430iz2 [1, 0, 0, -194776, -32214820] [2, 2] 3538944  
248430.iz4 248430iz3 [1, 0, 0, 53654, -108681574] [2] 7077888  
248430.iz1 248430iz4 [1, 0, 0, -3093126, -2094101010] [2] 7077888  

Rank

sage: E.rank()
 

The elliptic curves in class 248430iz have rank \(0\).

Complex multiplication

The elliptic curves in class 248430iz do not have complex multiplication.

Modular form 248430.2.a.iz

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

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.