Properties

Base field \(\Q(\zeta_{15})^+\)
Label 4.4.1125.1-145.2-a
Conductor 145.2
Rank \( 0 \)

Related objects

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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 145.2-a over \(\Q(\zeta_{15})^+\)

Isogeny class 145.2-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
145.2-a1 \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{2} - 2\) , \( 1099 a^{3} + 913 a^{2} - 3824 a - 2786\) , \( -37826 a^{3} - 3784 a^{2} + 135356 a - 3950\bigr] \)
145.2-a2 \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{2} - 2\) , \( -336 a^{3} + 433 a^{2} + 1271 a - 1711\) , \( -5858 a^{3} + 7041 a^{2} + 21967 a - 27908\bigr] \)
145.2-a3 \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{2} - 2\) , \( 59 a^{3} + 68 a^{2} - 194 a - 226\) , \( -383 a^{3} - 170 a^{2} + 1345 a + 448\bigr] \)
145.2-a4 \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{2} - 2\) , \( -16 a^{3} + 28 a^{2} + 71 a - 116\) , \( 116 a^{3} - 136 a^{2} - 441 a + 560\bigr] \)
145.2-a5 \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{2} - 2\) , \( -21 a^{3} + 28 a^{2} + 81 a - 106\) , \( -81 a^{3} + 99 a^{2} + 305 a - 391\bigr] \)
145.2-a6 \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{2} - 2\) , \( -26 a^{3} + 23 a^{2} + 91 a - 101\) , \( -108 a^{3} + 85 a^{2} + 375 a - 402\bigr] \)
145.2-a7 \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{2} - 2\) , \( -a^{3} + 3 a^{2} + 6 a - 6\) , \( 2 a^{2} + 2 a - 4\bigr] \)
145.2-a8 \( \bigl[a^{3} + a^{2} - 3 a - 1\) , \( -a^{3} + a^{2} + 4 a - 1\) , \( a^{2} - 2\) , \( 219 a^{3} - 137 a^{2} - 804 a + 574\) , \( -436 a^{3} - 152 a^{2} + 1498 a + 338\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph