Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-576.6-n
Conductor 576.6
Rank not recorded

Related objects

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Base field \(\Q(\sqrt{17}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).

Elliptic curves in class 576.6-n over \(\Q(\sqrt{17}) \)

Isogeny class 576.6-n contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
576.6-n1 \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -19 a - 36\) , \( 66 a + 110\bigr] \)
576.6-n2 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 294 a + 455\) , \( -43002 a - 67154\bigr] \)
576.6-n3 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 28 a + 52\) , \( 175 a + 261\bigr] \)
576.6-n4 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -7 a - 13\) , \( 0\bigr] \)
576.6-n5 \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 271 a - 686\) , \( 3406 a - 8718\bigr] \)
576.6-n6 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 39 a - 110\) , \( -192 a + 492\bigr] \)
576.6-n7 \( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -23 a - 40\) , \( -94 a - 160\bigr] \)
576.6-n8 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -36 a + 25\) , \( -702 a + 1986\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph