Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("248430.t1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 248430t

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
248430.t7 248430t1 [1, 1, 0, -339693, 26672157] [2] 5308416 \(\Gamma_0(N)\)-optimal
248430.t5 248430t2 [1, 1, 0, -2989613, -1971897507] [2, 2] 10616832  
248430.t4 248430t3 [1, 1, 0, -22201533, 40255240173] [2] 15925248  
248430.t6 248430t4 [1, 1, 0, -670933, -4949546363] [2] 21233664  
248430.t2 248430t5 [1, 1, 0, -47707013, -126849708747] [2] 21233664  
248430.t3 248430t6 [1, 1, 0, -22367153, 39623929857] [2, 2] 31850496  
248430.t8 248430t7 [1, 1, 0, 6036677, 133419057283] [2] 63700992  
248430.t1 248430t8 [1, 1, 0, -53420903, -94571745393] [2] 63700992  

Rank

sage: E.rank()
 

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

Modular form 248430.2.a.t

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

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.