Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-576.7-n
Conductor 576.7
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 576.7-n over \(\Q(\sqrt{17}) \)

Isogeny class 576.7-n contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
576.7-n1 \( \bigl[a\) , \( 1\) , \( a\) , \( 21 a - 61\) , \( 93 a - 253\bigr] \)
576.7-n2 \( \bigl[a\) , \( -1\) , \( a\) , \( 34 a - 9\) , \( 701 a + 1285\bigr] \)
576.7-n3 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -25 a + 75\) , \( -100 a + 257\bigr] \)
576.7-n4 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 10 a - 25\) , \( -25 a + 61\bigr] \)
576.7-n5 \( \bigl[a\) , \( -1\) , \( a\) , \( -41 a - 69\) , \( 191 a + 301\bigr] \)
576.7-n6 \( \bigl[a\) , \( a\) , \( a\) , \( -268 a - 420\) , \( -3824 a - 5972\bigr] \)
576.7-n7 \( \bigl[a\) , \( a\) , \( a\) , \( 22 a - 60\) , \( -124 a + 316\bigr] \)
576.7-n8 \( \bigl[a\) , \( -1\) , \( a\) , \( -296 a + 751\) , \( 43001 a - 110155\bigr] \)

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