Properties

Label 435120.i
Number of curves $6$
Conductor $435120$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("435120.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 435120.i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
435120.i1 435120i3 [0, -1, 0, -267347936, 1682621243136] [2] 63700992 \(\Gamma_0(N)\)-optimal*
435120.i2 435120i6 [0, -1, 0, -237650016, -1403906400000] [2] 127401984  
435120.i3 435120i4 [0, -1, 0, -22990816, 4773134080] [2, 2] 63700992  
435120.i4 435120i2 [0, -1, 0, -16718816, 26263514880] [2, 2] 31850496 \(\Gamma_0(N)\)-optimal*
435120.i5 435120i1 [0, -1, 0, -662496, 714698496] [2] 15925248 \(\Gamma_0(N)\)-optimal*
435120.i6 435120i5 [0, -1, 0, 91316384, 37967944960] [2] 127401984  
*optimality has not been proved rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 3 curves highlighted, and conditionally curve 435120.i5.

Rank

sage: E.rank()
 

The elliptic curves in class 435120.i have rank \(0\).

Modular form 435120.2.a.i

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} + q^{9} - 4q^{11} + 2q^{13} + q^{15} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.