Properties

Base field 4.4.10512.1
Label 4.4.10512.1-4.1-d
Conductor 4.1
Rank not recorded

Related objects

Learn more about

Base field 4.4.10512.1

Generator \(a\), with minimal polynomial \( x^{4} - 7 x^{2} - 6 x + 1 \); class number \(1\).

Elliptic curves in class 4.1-d over 4.4.10512.1

Isogeny class 4.1-d contains 6 curves linked by isogenies of degrees dividing 45.

Curve label Weierstrass Coefficients
4.1-d1 \( \bigl[a^{3} - 5 a - 4\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( a^{3} - a^{2} - 5 a - 1\) , \( 1947 a^{3} - 2429 a^{2} - 10567 a + 1563\) , \( -49250 a^{3} + 61634 a^{2} + 267701 a - 39371\bigr] \)
4.1-d2 \( \bigl[a^{3} - a^{2} - 5 a - 1\) , \( a^{3} - a^{2} - 6 a\) , \( a^{3} - a^{2} - 5 a\) , \( 1836 a^{3} + 309 a^{2} - 13053 a - 13482\) , \( 86043 a^{3} + 13803 a^{2} - 599155 a - 604835\bigr] \)
4.1-d3 \( \bigl[a^{3} - a^{2} - 5 a - 1\) , \( a + 1\) , \( a^{3} - a^{2} - 5 a\) , \( 2253 a^{3} - 4398 a^{2} - 7392 a + 1116\) , \( 116795 a^{3} - 216641 a^{2} - 415035 a + 63335\bigr] \)
4.1-d4 \( \bigl[a^{3} - a^{2} - 4 a - 1\) , \( a^{3} - 6 a - 6\) , \( a^{3} - 6 a - 4\) , \( 43 a^{3} - 48 a^{2} - 206 a - 90\) , \( 45 a^{3} - 287 a^{2} + 192 a + 798\bigr] \)
4.1-d5 \( \bigl[a\) , \( a^{2} - 2 a - 5\) , \( 1\) , \( 39 a^{3} - 35 a^{2} - 200 a - 120\) , \( -8 a^{3} + 142 a^{2} - 187 a - 471\bigr] \)
4.1-d6 \( \bigl[a\) , \( a^{2} - 2 a - 5\) , \( 1\) , \( -a^{3} + 5 a + 5\) , \( a + 1\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 3 & 3 & 15 & 15 & 5 \\ 3 & 1 & 9 & 5 & 45 & 15 \\ 3 & 9 & 1 & 45 & 5 & 15 \\ 15 & 5 & 45 & 1 & 9 & 3 \\ 15 & 45 & 5 & 9 & 1 & 3 \\ 5 & 15 & 15 & 3 & 3 & 1 \end{array}\right)\)

Isogeny graph