Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-676.4-g
Conductor 676.4
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 676.4-g over \(\Q(\sqrt{17}) \)

Isogeny class 676.4-g contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
676.4-g1 \( \bigl[1\) , \( a\) , \( a + 1\) , \( 195 a - 943\) , \( 3156 a - 1246\bigr] \)
676.4-g2 \( \bigl[1\) , \( a\) , \( a + 1\) , \( 260 a - 618\) , \( 2914 a - 7630\bigr] \)
676.4-g3 \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -1636 a - 2617\) , \( 22417 a + 35149\bigr] \)
676.4-g4 \( \bigl[1\) , \( a\) , \( a + 1\) , \( 10 a - 48\) , \( 26 a - 126\bigr] \)
676.4-g5 \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -31 a + 78\) , \( 4838 a - 12394\bigr] \)
676.4-g6 \( \bigl[1\) , \( a\) , \( a + 1\) , \( 25 a - 623\) , \( -538 a + 5946\bigr] \)
676.4-g7 \( \bigl[1\) , \( 1\) , \( 0\) , \( 970 a - 2485\) , \( -13672 a + 35021\bigr] \)
676.4-g8 \( \bigl[1\) , \( -a + 1\) , \( a\) , \( 254 a - 707\) , \( -131173 a + 336189\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 6 & 12 & 2 & 12 & 4 \\ 3 & 1 & 12 & 2 & 4 & 6 & 4 & 12 \\ 4 & 12 & 1 & 6 & 12 & 2 & 3 & 4 \\ 6 & 2 & 6 & 1 & 2 & 3 & 2 & 6 \\ 12 & 4 & 12 & 2 & 1 & 6 & 4 & 3 \\ 2 & 6 & 2 & 3 & 6 & 1 & 6 & 2 \\ 12 & 4 & 3 & 2 & 4 & 6 & 1 & 12 \\ 4 & 12 & 4 & 6 & 3 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph