Properties

Base field 3.3.785.1
Label 3.3.785.1-15.2-b
Conductor 15.2
Rank \( 0 \)

Related objects

Learn more

Base field 3.3.785.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 6 x + 5 \); class number \(1\).

Elliptic curves in class 15.2-b over 3.3.785.1

Isogeny class 15.2-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
15.2-b1 \( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 3\) , \( 1\) , \( 255 a^{2} - 30 a - 1607\) , \( 4253 a^{2} - 756 a - 26252\bigr] \)
15.2-b2 \( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 3\) , \( 1\) , \( -75 a^{2} + 300 a - 277\) , \( -1077 a^{2} + 3914 a - 2954\bigr] \)
15.2-b3 \( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 3\) , \( 1\) , \( 10 a^{2} + 15 a - 102\) , \( 74 a^{2} + 23 a - 549\bigr] \)
15.2-b4 \( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 3\) , \( 1\) , \( 3\) , \( 2 a^{2} - 12\bigr] \)
15.2-b5 \( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 3\) , \( 1\) , \( 8\) , \( 2 a + 1\bigr] \)
15.2-b6 \( \bigl[a^{2} + a - 4\) , \( -a^{2} + a + 3\) , \( 1\) , \( -10 a^{2} - 15 a + 28\) , \( 18 a^{2} + 29 a - 47\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 4 & 2 & 4 & 8 & 8 \\ 4 & 1 & 2 & 4 & 8 & 8 \\ 2 & 2 & 1 & 2 & 4 & 4 \\ 4 & 4 & 2 & 1 & 2 & 2 \\ 8 & 8 & 4 & 2 & 1 & 4 \\ 8 & 8 & 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph