Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-67600.6-f
Conductor 67600.6
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{-1}) \)

Generator \(i\), with minimal polynomial \( x^{2} + 1 \); class number \(1\).

Elliptic curves in class 67600.6-f over \(\Q(\sqrt{-1}) \)

Isogeny class 67600.6-f contains 10 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
67600.6-f1 \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -670 i + 143\) , \( 3211 i - 5832\bigr] \)
67600.6-f2 \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -370 i - 577\) , \( -5521 i - 4344\bigr] \)
67600.6-f3 \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -40 i - 17\) , \( -47 i - 176\bigr] \)
67600.6-f4 \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -100 i - 887\) , \( -9827 i + 3354\bigr] \)
67600.6-f5 \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -700 i + 553\) , \( 10213 i - 126\bigr] \)
67600.6-f6 \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( 20 i + 8\) , \( -3 i - 45\bigr] \)
67600.6-f7 \( \bigl[0\) , \( 0\) , \( 0\) , \( -24 i - 10\) , \( -46 i + 9\bigr] \)
67600.6-f8 \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( 320 i + 133\) , \( -413 i - 2610\bigr] \)
67600.6-f9 \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -5920 i - 9227\) , \( -338111 i - 286714\bigr] \)
67600.6-f10 \( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -10720 i + 2293\) , \( 200881 i - 388642\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph