Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-2268.2-b
Conductor 2268.2
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 2268.2-b over \(\Q(\sqrt{-7}) \)

Isogeny class 2268.2-b contains 12 curves linked by isogenies of degrees dividing 36.

Curve label Weierstrass Coefficients
2268.2-b1 \( \bigl[1\) , \( -1\) , \( 1\) , \( -1535\) , \( 23591\bigr] \)
2268.2-b2 \( \bigl[1\) , \( -1\) , \( 1\) , \( -90 a + 145\) , \( 170 a + 615\bigr] \)
2268.2-b3 \( \bigl[1\) , \( -1\) , \( 1\) , \( 90 a + 55\) , \( -170 a + 785\bigr] \)
2268.2-b4 \( \bigl[1\) , \( -1\) , \( 1\) , \( 10\) , \( 10 a - 7\bigr] \)
2268.2-b5 \( \bigl[1\) , \( -1\) , \( 1\) , \( 10\) , \( -10 a + 3\bigr] \)
2268.2-b6 \( \bigl[1\) , \( -1\) , \( 1\) , \( -5\) , \( -7\bigr] \)
2268.2-b7 \( \bigl[1\) , \( -1\) , \( 1\) , \( 40\) , \( 155\bigr] \)
2268.2-b8 \( \bigl[1\) , \( -1\) , \( 1\) , \( 270 a - 350\) , \( 710 a + 3621\bigr] \)
2268.2-b9 \( \bigl[1\) , \( -1\) , \( 1\) , \( -270 a - 80\) , \( -710 a + 4331\bigr] \)
2268.2-b10 \( \bigl[1\) , \( -1\) , \( 1\) , \( -320\) , \( 1883\bigr] \)
2268.2-b11 \( \bigl[1\) , \( -1\) , \( 1\) , \( -95\) , \( -331\bigr] \)
2268.2-b12 \( \bigl[1\) , \( -1\) , \( 1\) , \( -24575\) , \( 1488935\bigr] \)

Rank

Rank: \( 0 \)

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