Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-14112.5-b
Conductor 14112.5
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{-7}) \)

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

Elliptic curves in class 14112.5-b over \(\Q(\sqrt{-7}) \)

Isogeny class 14112.5-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
14112.5-b1 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 189 a + 10\) , \( 364 a + 1336\bigr] \)
14112.5-b2 \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 83 a - 28\) , \( 438 a + 584\bigr] \)
14112.5-b3 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 202 a - 142\) , \( 1070 a + 534\bigr] \)
14112.5-b4 \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -8107 a + 2702\) , \( 69654 a + 105416\bigr] \)
14112.5-b5 \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 2183 a - 728\) , \( 9286 a + 12120\bigr] \)
14112.5-b6 \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 19193 a - 6398\) , \( -662042 a - 967656\bigr] \)
14112.5-b7 \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 1763 a - 588\) , \( 18806 a + 26120\bigr] \)
14112.5-b8 \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 28223 a - 9408\) , \( 1197158 a + 1712504\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph