Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-272.5-a
Conductor 272.5
Rank \( 0 \)

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 272.5-a over \(\Q(\sqrt{17}) \)

Isogeny class 272.5-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
272.5-a1 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 714 a - 2424\) , \( -20585 a + 47480\bigr] \)
272.5-a2 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -a - 4\) , \( -69 a - 56\bigr] \)
272.5-a3 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 39 a + 60\) , \( 67 a + 104\bigr] \)
272.5-a4 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -a - 4\) , \( a\bigr] \)
272.5-a5 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -6 a - 24\) , \( -19 a - 16\bigr] \)
272.5-a6 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -15 a + 36\) , \( 15 a - 40\bigr] \)
272.5-a7 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -91 a - 364\) , \( -1549 a - 1240\bigr] \)
272.5-a8 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -2256 a - 3744\) , \( -85533 a - 132376\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph