Properties

Label 248430hi
Number of curves 8
Conductor 248430
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("248430.hi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 248430hi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
248430.hi7 248430hi1 [1, 1, 1, -4119970, -3219245905] [2] 10616832 \(\Gamma_0(N)\)-optimal
248430.hi6 248430hi2 [1, 1, 1, -4782450, -2115289233] [2, 2] 21233664  
248430.hi5 248430hi3 [1, 1, 1, -12193945, 12450724775] [2] 31850496  
248430.hi4 248430hi4 [1, 1, 1, -36084630, 81949845375] [2] 42467328  
248430.hi8 248430hi5 [1, 1, 1, 15920050, -15513947233] [2] 42467328  
248430.hi2 248430hi6 [1, 1, 1, -181788825, 943255264167] [2, 2] 63700992  
248430.hi1 248430hi7 [1, 1, 1, -2908556505, 60374792910375] [2] 127401984  
248430.hi3 248430hi8 [1, 1, 1, -168539225, 1086600036647] [2] 127401984  

Rank

sage: E.rank()
 

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

Modular form 248430.2.a.hi

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} - q^{12} - q^{15} + q^{16} + 6q^{17} + q^{18} + 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.