Properties

Base field 3.3.316.1
Label 3.3.316.1-37.1-b
Conductor 37.1
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 37.1-b over 3.3.316.1

Isogeny class 37.1-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
37.1-b1 \( \bigl[a^{2} + a - 3\) , \( a^{2} - a - 4\) , \( 0\) , \( -31 a^{2} - 107 a - 94\) , \( 323 a^{2} + 821 a + 427\bigr] \)
37.1-b2 \( \bigl[a^{2} + a - 3\) , \( a^{2} - a - 4\) , \( 0\) , \( -66 a^{2} - 92 a + 51\) , \( 494 a^{2} + 672 a - 406\bigr] \)
37.1-b3 \( \bigl[a^{2} + a - 3\) , \( -a + 1\) , \( a + 1\) , \( 272629937 a^{2} - 144307547 a - 1158442916\) , \( 3583317227543 a^{2} - 1896709220400 a - 15226018492530\bigr] \)
37.1-b4 \( \bigl[a^{2} + a - 3\) , \( -a + 1\) , \( a + 1\) , \( 17039757 a^{2} - 9019427 a - 72404321\) , \( 55994592296 a^{2} - 29638866100 a - 237928892040\bigr] \)
37.1-b5 \( \bigl[a^{2} + a - 3\) , \( -a^{2} + 3\) , \( a + 1\) , \( -19221 a^{2} + 2696 a + 68110\) , \( -9776007 a^{2} + 5673613 a + 42444636\bigr] \)
37.1-b6 \( \bigl[1\) , \( a^{2} - a - 4\) , \( 0\) , \( 2754 a^{2} - 1458 a - 11702\) , \( 83572 a^{2} - 44236 a - 355109\bigr] \)
37.1-b7 \( \bigl[1\) , \( a^{2} - a - 4\) , \( 0\) , \( -6616 a^{2} + 3502 a + 28113\) , \( 561018 a^{2} - 296956 a - 2383844\bigr] \)
37.1-b8 \( \bigl[1\) , \( -a - 1\) , \( a^{2} - 3\) , \( 6552923945 a^{2} - 3468571292 a - 27844294777\) , \( 546134280974000 a^{2} - 289077929896281 a - 2320601312548858\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph