Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-24.1-b
Conductor 24.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{3}) \)

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

Elliptic curves in class 24.1-b over \(\Q(\sqrt{3}) \)

Isogeny class 24.1-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
24.1-b1 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 1033 a - 1794\) , \( 24484 a - 42410\bigr] \)
24.1-b2 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -17 a + 26\) , \( -338 a + 584\bigr] \)
24.1-b3 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -38 a + 66\) , \( 168 a - 291\bigr] \)
24.1-b4 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 3 a - 9\) , \( 7 a - 14\bigr] \)
24.1-b5 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 23 a - 44\) , \( -68 a + 116\bigr] \)
24.1-b6 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 63 a - 114\) , \( 412 a - 716\bigr] \)
24.1-b7 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 383 a - 674\) , \( -5198 a + 9008\bigr] \)
24.1-b8 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 53 a - 114\) , \( 460 a - 830\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph