Properties

Base field 3.3.316.1
Label 3.3.316.1-32.1-a
Conductor 32.1
Rank not recorded

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Base field 3.3.316.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 4 x + 2 \); class number \(1\).

Elliptic curves in class 32.1-a over 3.3.316.1

Isogeny class 32.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
32.1-a1 \( \bigl[a^{2} - 2\) , \( -a^{2} - a + 2\) , \( a^{2} - 2\) , \( -602 a^{2} + 318 a + 2556\) , \( 12985 a^{2} - 6874 a - 55177\bigr] \)
32.1-a2 \( \bigl[a\) , \( a^{2} + a - 2\) , \( a\) , \( 68 a^{2} - 33 a - 285\) , \( -445 a^{2} + 236 a + 1891\bigr] \)
32.1-a3 \( \bigl[a\) , \( a^{2} + a - 2\) , \( a\) , \( 13 a^{2} - 3 a - 50\) , \( 19 a^{2} - 7 a - 76\bigr] \)
32.1-a4 \( \bigl[a\) , \( -a^{2} + a + 2\) , \( a\) , \( 14434589287 a^{2} - 7640467435 a - 61334598487\) , \( 1856721004039097 a^{2} - 982793212111362 a - 7889468486259131\bigr] \)
32.1-a5 \( \bigl[a\) , \( -a^{2} + a + 4\) , \( a\) , \( 26100179 a^{2} - 13815259 a - 110903333\) , \( 106175166175 a^{2} - 56200275854 a - 451153202737\bigr] \)
32.1-a6 \( \bigl[a\) , \( -a^{2} + a + 4\) , \( a\) , \( 1631309 a^{2} - 863479 a - 6931663\) , \( 1660636815 a^{2} - 879002600 a - 7056279211\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph