Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-1792.5-b
Conductor 1792.5
Rank \( 1 \)

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 1792.5-b over \(\Q(\sqrt{-7}) \)

Isogeny class 1792.5-b contains 12 curves linked by isogenies of degrees dividing 36.

Curve label Weierstrass Coefficients
1792.5-b1 \( \bigl[0\) , \( -1\) , \( 0\) , \( -2728\) , \( 55920\bigr] \)
1792.5-b2 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -159 a + 258\) , \( 370 a + 1352\bigr] \)
1792.5-b3 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 161 a + 98\) , \( -210 a + 1820\bigr] \)
1792.5-b4 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 18\) , \( 30 a - 4\bigr] \)
1792.5-b5 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( a + 18\) , \( -30 a + 8\bigr] \)
1792.5-b6 \( \bigl[0\) , \( -1\) , \( 0\) , \( -8\) , \( -16\bigr] \)
1792.5-b7 \( \bigl[0\) , \( -1\) , \( 0\) , \( 72\) , \( 368\bigr] \)
1792.5-b8 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 481 a - 622\) , \( 1730 a + 8904\bigr] \)
1792.5-b9 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -479 a - 142\) , \( -2210 a + 10492\bigr] \)
1792.5-b10 \( \bigl[0\) , \( -1\) , \( 0\) , \( -568\) , \( 4464\bigr] \)
1792.5-b11 \( \bigl[0\) , \( -1\) , \( 0\) , \( -168\) , \( -784\bigr] \)
1792.5-b12 \( \bigl[0\) , \( -1\) , \( 0\) , \( -43688\) , \( 3529328\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrrrr} 1 & 6 & 6 & 18 & 18 & 9 & 3 & 2 & 2 & 6 & 18 & 2 \\ 6 & 1 & 4 & 12 & 3 & 6 & 2 & 3 & 12 & 4 & 12 & 12 \\ 6 & 4 & 1 & 3 & 12 & 6 & 2 & 12 & 3 & 4 & 12 & 12 \\ 18 & 12 & 3 & 1 & 4 & 2 & 6 & 36 & 9 & 12 & 4 & 36 \\ 18 & 3 & 12 & 4 & 1 & 2 & 6 & 9 & 36 & 12 & 4 & 36 \\ 9 & 6 & 6 & 2 & 2 & 1 & 3 & 18 & 18 & 6 & 2 & 18 \\ 3 & 2 & 2 & 6 & 6 & 3 & 1 & 6 & 6 & 2 & 6 & 6 \\ 2 & 3 & 12 & 36 & 9 & 18 & 6 & 1 & 4 & 12 & 36 & 4 \\ 2 & 12 & 3 & 9 & 36 & 18 & 6 & 4 & 1 & 12 & 36 & 4 \\ 6 & 4 & 4 & 12 & 12 & 6 & 2 & 12 & 12 & 1 & 3 & 3 \\ 18 & 12 & 12 & 4 & 4 & 2 & 6 & 36 & 36 & 3 & 1 & 9 \\ 2 & 12 & 12 & 36 & 36 & 18 & 6 & 4 & 4 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph