Properties

Base field 3.3.316.1
Label 3.3.316.1-242.3-b
Conductor 242.3
Rank \( 0 \)

Related objects

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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 242.3-b over 3.3.316.1

Isogeny class 242.3-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
242.3-b1 \( \bigl[a^{2} + a - 3\) , \( a^{2} - 4\) , \( a^{2} - 3\) , \( -17089005789166286516 a^{2} + 9045494102123436959 a + 72613587255077018672\) , \( 239491187919164651072372415896 a^{2} - 126766656560365448750343743032 a - 1017631715112124311122237879909\bigr] \)
242.3-b2 \( \bigl[a^{2} + a - 3\) , \( -a + 1\) , \( a\) , \( 163201859571 a^{2} - 86385450180 a - 693467637401\) , \( 52479892685555807 a^{2} - 27778477321846893 a - 222994439446883602\bigr] \)
242.3-b3 \( \bigl[a^{2} + a - 3\) , \( -a + 1\) , \( a\) , \( 10200132836 a^{2} - 5399099430 a - 43341797926\) , \( 820000263652323 a^{2} - 434039735261194 a - 3484296361562003\bigr] \)
242.3-b4 \( \bigl[1\) , \( a^{2} + a - 4\) , \( 1\) , \( 100 a^{2} + 76 a - 721\) , \( 1048 a^{2} + 485 a - 6877\bigr] \)
242.3-b5 \( \bigl[1\) , \( a\) , \( a + 1\) , \( 20203900862562389334443 a^{2} - 10694259709833632274695 a - 85849214183464417082380\) , \( -2285799641956889659257421153575487 a^{2} + 1209911649340346379381685404090182 a + 9712683920681029332844506518986769\bigr] \)
242.3-b6 \( \bigl[1\) , \( a\) , \( a + 1\) , \( 1331292997660594700983 a^{2} - 704675456671176969100 a - 5656851044487640237345\) , \( -31621800609835111873402107774674 a^{2} + 16737943356313969364667113002303 a + 134365474859900078732316315405433\bigr] \)
242.3-b7 \( \bigl[1\) , \( a + 1\) , \( a^{2} - 2\) , \( -26140776857754976733142982 a^{2} + 13836746608257972575168441 a + 111075834644485451677761735\) , \( -176958717384573892178034799698113749293 a^{2} + 93667183109988451030481895839197063871 a + 751922459614203146023948231356362753108\bigr] \)
242.3-b8 \( \bigl[1\) , \( -a^{2} + a + 3\) , \( 0\) , \( 41761256065998246 a^{2} - 22104925242738941 a - 177449446073241693\) , \( 6321701762221270525137686 a^{2} - 3346181557373420332949796 a - 26861799227819409800534166\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 8 & 4 & 8 & 8 & 4 & 8 & 2 \\ 8 & 1 & 2 & 4 & 16 & 8 & 16 & 4 \\ 4 & 2 & 1 & 2 & 8 & 4 & 8 & 2 \\ 8 & 4 & 2 & 1 & 16 & 8 & 16 & 4 \\ 8 & 16 & 8 & 16 & 1 & 2 & 4 & 4 \\ 4 & 8 & 4 & 8 & 2 & 1 & 2 & 2 \\ 8 & 16 & 8 & 16 & 4 & 2 & 1 & 4 \\ 2 & 4 & 2 & 4 & 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph