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Properties

Base field \(\Q(\sqrt{-23}) \)
Label 2.0.23.1-108.6-c
Conductor 108.6
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{-23}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 6 \); class number \(3\).

Elliptic curves in class 108.6-c over \(\Q(\sqrt{-23}) \)

Isogeny class 108.6-c contains 12 curves linked by isogenies of degrees dividing 24.

Curve label Weierstrass Coefficients
108.6-c1 \( \bigl[a\) , \( 0\) , \( a\) , \( -855 a + 3588\) , \( 24741 a + 54133\bigr] \)
108.6-c2 \( \bigl[1\) , \( a - 1\) , \( 1\) , \( -96 a + 958\) , \( -4007 a - 1907\bigr] \)
108.6-c3 \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -38 a - 1175\) , \( 758 a + 15755\bigr] \)
108.6-c4 \( \bigl[1\) , \( -1\) , \( a + 1\) , \( -38 a + 40\) , \( 353 a - 2065\bigr] \)
108.6-c5 \( \bigl[1\) , \( a - 1\) , \( 1\) , \( 4 a - 2\) , \( 13 a + 55\bigr] \)
108.6-c6 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 57 a + 394\) , \( 459 a - 4141\bigr] \)
108.6-c7 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 42 a - 461\) , \( 1149 a - 1531\bigr] \)
108.6-c8 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 2 a + 139\) , \( 269 a - 427\bigr] \)
108.6-c9 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -3 a - 146\) , \( -21 a - 397\bigr] \)
108.6-c10 \( \bigl[a\) , \( 0\) , \( a\) , \( -55 a + 228\) , \( 421 a + 757\bigr] \)
108.6-c11 \( \bigl[1\) , \( a - 1\) , \( 1\) , \( -6 a + 58\) , \( -47 a - 35\bigr] \)
108.6-c12 \( \bigl[1\) , \( a - 1\) , \( 1\) , \( 4 a - 137\) , \( -17 a - 575\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrrrr} 1 & 24 & 12 & 24 & 4 & 8 & 3 & 6 & 4 & 2 & 12 & 8 \\ 24 & 1 & 8 & 4 & 24 & 3 & 8 & 4 & 6 & 12 & 2 & 12 \\ 12 & 8 & 1 & 8 & 3 & 24 & 4 & 2 & 12 & 6 & 4 & 24 \\ 24 & 4 & 8 & 1 & 24 & 12 & 8 & 4 & 6 & 12 & 2 & 3 \\ 4 & 24 & 3 & 24 & 1 & 8 & 12 & 6 & 4 & 2 & 12 & 8 \\ 8 & 3 & 24 & 12 & 8 & 1 & 24 & 12 & 2 & 4 & 6 & 4 \\ 3 & 8 & 4 & 8 & 12 & 24 & 1 & 2 & 12 & 6 & 4 & 24 \\ 6 & 4 & 2 & 4 & 6 & 12 & 2 & 1 & 6 & 3 & 2 & 12 \\ 4 & 6 & 12 & 6 & 4 & 2 & 12 & 6 & 1 & 2 & 3 & 2 \\ 2 & 12 & 6 & 12 & 2 & 4 & 6 & 3 & 2 & 1 & 6 & 4 \\ 12 & 2 & 4 & 2 & 12 & 6 & 4 & 2 & 3 & 6 & 1 & 6 \\ 8 & 12 & 24 & 3 & 8 & 4 & 24 & 12 & 2 & 4 & 6 & 1 \end{array}\right)\)

Isogeny graph