Properties

Base field \(\Q(\zeta_{15})^+\)
Label 4.4.1125.1-45.1-b
Conductor 45.1
Rank not recorded

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Base field \(\Q(\zeta_{15})^+\)

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 4 x^{2} + 4 x + 1 \); class number \(1\).

Elliptic curves in class 45.1-b over \(\Q(\zeta_{15})^+\)

Isogeny class 45.1-b contains 10 curves linked by isogenies of degrees dividing 32.

Curve label Weierstrass Coefficients
45.1-b1 \( \bigl[1\) , \( 1\) , \( 1\) , \( -14490 a^{3} + 43470 a - 25605\) , \( -1094688 a^{3} + 3284064 a - 1810794\bigr] \)
45.1-b2 \( \bigl[1\) , \( 1\) , \( 1\) , \( 14490 a^{3} - 43470 a - 11115\) , \( 1094688 a^{3} - 3284064 a - 716106\bigr] \)
45.1-b3 \( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \)
45.1-b4 \( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \)
45.1-b5 \( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \)
45.1-b6 \( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \)
45.1-b7 \( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \)
45.1-b8 \( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \)
45.1-b9 \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
45.1-b10 \( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrr} 1 & 4 & 2 & 4 & 8 & 32 & 8 & 16 & 32 & 16 \\ 4 & 1 & 2 & 4 & 8 & 32 & 8 & 16 & 32 & 16 \\ 2 & 2 & 1 & 2 & 4 & 16 & 4 & 8 & 16 & 8 \\ 4 & 4 & 2 & 1 & 2 & 8 & 2 & 4 & 8 & 4 \\ 8 & 8 & 4 & 2 & 1 & 16 & 4 & 8 & 16 & 8 \\ 32 & 32 & 16 & 8 & 16 & 1 & 4 & 2 & 4 & 8 \\ 8 & 8 & 4 & 2 & 4 & 4 & 1 & 2 & 4 & 2 \\ 16 & 16 & 8 & 4 & 8 & 2 & 2 & 1 & 2 & 4 \\ 32 & 32 & 16 & 8 & 16 & 4 & 4 & 2 & 1 & 8 \\ 16 & 16 & 8 & 4 & 8 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph