Properties

Base field \(\Q(\zeta_{15})^+\)
Label 4.4.1125.1-145.1-f
Conductor 145.1
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 145.1-f over \(\Q(\zeta_{15})^+\)

Isogeny class 145.1-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
145.1-f1 \( \bigl[a^{2} - 2\) , \( a - 1\) , \( a^{3} - 2 a\) , \( -400 a^{3} + 537 a^{2} + 1505 a - 2104\) , \( 8354 a^{3} - 9885 a^{2} - 31265 a + 39200\bigr] \)
145.1-f2 \( \bigl[a^{2} - 2\) , \( a - 1\) , \( a^{3} - 2 a\) , \( 490 a^{3} + 187 a^{2} - 1775 a - 524\) , \( 8376 a^{3} + 2719 a^{2} - 29553 a - 5506\bigr] \)
145.1-f3 \( \bigl[a^{2} - 2\) , \( a - 1\) , \( a^{3} - 2 a\) , \( 5 a^{3} + 42 a^{2} - 15 a - 154\) , \( 261 a^{3} - 113 a^{2} - 949 a + 525\bigr] \)
145.1-f4 \( \bigl[a^{2} - 2\) , \( a - 1\) , \( a^{3} - 2 a\) , \( 2 a^{2} - 9\) , \( 4 a^{3} - 3 a^{2} - 14 a + 9\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph