Properties

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

Isogeny class 145.1-b contains 4 curves linked by isogenies of degrees dividing 14.

Curve label Weierstrass Coefficients
145.1-b1 \( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{2} + a - 2\) , \( 3 a^{2} - a - 7\) , \( a^{3} + 2 a^{2} - 4 a - 5\bigr] \)
145.1-b2 \( \bigl[a^{2} + a - 2\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{2} + a - 2\) , \( -10 a^{3} - 2 a^{2} + 34 a + 3\) , \( -9 a^{3} - 2 a^{2} + 31 a - 2\bigr] \)
145.1-b3 \( \bigl[a + 1\) , \( -a^{3} + 2 a - 1\) , \( a^{3} + a^{2} - 2 a - 2\) , \( -16838 a^{3} - 21557 a^{2} + 25365 a + 6059\) , \( 3201633 a^{3} + 3227005 a^{2} - 6714610 a - 1515432\bigr] \)
145.1-b4 \( \bigl[a + 1\) , \( -a^{3} + 2 a - 1\) , \( a^{3} + a^{2} - 2 a - 2\) , \( -503858 a^{3} - 424367 a^{2} + 1237475 a + 272614\) , \( 278727121 a^{3} + 231111633 a^{2} - 692450628 a - 152315529\bigr] \)

Rank

Rank: \( 0 \)

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