Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-612.1-e
Conductor 612.1
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 612.1-e over \(\Q(\sqrt{17}) \)

Isogeny class 612.1-e contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
612.1-e1 \( \bigl[1\) , \( 0\) , \( 0\) , \( -1644\) , \( -30942\bigr] \)
612.1-e2 \( \bigl[1\) , \( 1\) , \( 1\) , \( 86 a + 131\) , \( 2522 a + 3939\bigr] \)
612.1-e3 \( \bigl[1\) , \( 0\) , \( 0\) , \( 226\) , \( -2232\bigr] \)
612.1-e4 \( \bigl[1\) , \( 0\) , \( 0\) , \( -114\) , \( -396\bigr] \)
612.1-e5 \( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( 68\bigr] \)
612.1-e6 \( \bigl[1\) , \( 0\) , \( 0\) , \( -1734\) , \( -27936\bigr] \)
612.1-e7 \( \bigl[1\) , \( 1\) , \( 1\) , \( -86 a + 217\) , \( -2522 a + 6461\bigr] \)
612.1-e8 \( \bigl[1\) , \( 0\) , \( 0\) , \( -27744\) , \( -1781010\bigr] \)

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