Properties

Base field \(\Q(\zeta_{15})^+\)
Label 4.4.1125.1-145.2-d
Conductor 145.2
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 145.2-d over \(\Q(\zeta_{15})^+\)

Isogeny class 145.2-d contains 4 curves linked by isogenies of degrees dividing 14.

Curve label Weierstrass Coefficients
145.2-d1 \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} + a - 2\) , \( 0\) , \( -454771 a^{3} - 376071 a^{2} + 1131814 a + 248570\) , \( -229727262 a^{3} - 190004926 a^{2} + 571751738 a + 125731744\bigr] \)
145.2-d2 \( \bigl[a^{3} + a^{2} - 3 a - 2\) , \( a^{2} + a - 2\) , \( 0\) , \( -454716 a^{3} - 376136 a^{2} + 1131604 a + 248835\) , \( -229726834 a^{3} - 190005324 a^{2} + 571750203 a + 125733493\bigr] \)
145.2-d3 \( \bigl[a^{2} - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a + 1\) , \( -17 a^{3} + 22 a^{2} + 64 a - 84\) , \( 67 a^{3} - 79 a^{2} - 250 a + 314\bigr] \)
145.2-d4 \( \bigl[a^{2} - 1\) , \( a^{3} + a^{2} - 4 a - 1\) , \( a + 1\) , \( -2 a^{3} + 2 a^{2} + 4 a - 4\) , \( a^{3} - a^{2} - 6 a + 6\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 7 & 14 \\ 2 & 1 & 14 & 7 \\ 7 & 14 & 1 & 2 \\ 14 & 7 & 2 & 1 \end{array}\right)\)

Isogeny graph