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Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-7168.5-h
Conductor 7168.5
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 7168.5-h over \(\Q(\sqrt{-7}) \)

Isogeny class 7168.5-h contains 12 curves linked by isogenies of degrees dividing 36.

Curve label Weierstrass Coefficients
7168.5-h1 \( \bigl[0\) , \( a\) , \( 0\) , \( -2728 a + 5456\) , \( 55920 a + 111840\bigr] \)
7168.5-h2 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 418 a - 197\) , \( 2659 a + 2603\bigr] \)
7168.5-h3 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -62 a - 517\) , \( 673 a + 4701\bigr] \)
7168.5-h4 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 18 a - 37\) , \( 49 a - 67\bigr] \)
7168.5-h5 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 18 a - 37\) , \( -45 a + 75\bigr] \)
7168.5-h6 \( \bigl[0\) , \( a\) , \( 0\) , \( -8 a + 16\) , \( -16 a - 32\bigr] \)
7168.5-h7 \( \bigl[0\) , \( a\) , \( 0\) , \( 72 a - 144\) , \( 368 a + 736\bigr] \)
7168.5-h8 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -1102 a + 283\) , \( 13811 a + 12427\bigr] \)
7168.5-h9 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 338 a + 1243\) , \( 5105 a + 23485\bigr] \)
7168.5-h10 \( \bigl[0\) , \( a\) , \( 0\) , \( -568 a + 1136\) , \( 4464 a + 8928\bigr] \)
7168.5-h11 \( \bigl[0\) , \( a\) , \( 0\) , \( -168 a + 336\) , \( -784 a - 1568\bigr] \)
7168.5-h12 \( \bigl[0\) , \( a\) , \( 0\) , \( -43688 a + 87376\) , \( 3529328 a + 7058656\bigr] \)

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