Properties

Base field 3.3.733.1
Label 3.3.733.1-10.1-a
Conductor 10.1
Rank not recorded

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Base field 3.3.733.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 7 x + 8 \); class number \(1\).

Elliptic curves in class 10.1-a over 3.3.733.1

Isogeny class 10.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
10.1-a1 \( \bigl[a^{2} - 5\) , \( -a^{2} - a + 4\) , \( a\) , \( -254283425430303815 a^{2} - 386052765748533969 a + 807826405432831715\) , \( -128265428101555296555965052 a^{2} - 194732406112317607687625258 a + 407483104922159986550542545\bigr] \)
10.1-a2 \( \bigl[a^{2} - 5\) , \( -a^{2} - a + 4\) , \( a\) , \( -4049465429197136100 a^{2} - 6147893147574076769 a + 12864641476561585655\) , \( -8291016996382688583156230409 a^{2} - 12587411220000787426202062421 a + 26339516412587041281174042517\bigr] \)
10.1-a3 \( \bigl[1\) , \( -a\) , \( a^{2} - 4\) , \( -793533281 a^{2} - 1204741195 a + 2520955258\) , \( 11680631678321 a^{2} + 17733519821337 a - 37107895199680\bigr] \)
10.1-a4 \( \bigl[1\) , \( -a\) , \( a^{2} - 4\) , \( -10893142006 a^{2} - 16537954025 a + 34606139728\) , \( 1156292213663076 a^{2} + 1755481334824458 a - 3673394681594914\bigr] \)
10.1-a5 \( \bigl[a + 1\) , \( a - 1\) , \( a^{2} - 5\) , \( 4 a^{2} + 6 a - 8\) , \( 12 a^{2} + 18 a - 41\bigr] \)
10.1-a6 \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( 225468796079696669707481 a^{2} + 342306432946871581914275 a - 716285958340025181167230\) , \( -102770037091536501869102455441620105963 a^{2} - 156025336642090576588977058556709893561 a + 326487459846688471086063418466138671196\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph