Properties

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

Related objects

Learn more

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

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

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

Isogeny class 67600.6-i contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
67600.6-i1 \( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( 889 i + 1483\) , \( 19530 i - 21015\bigr] \)
67600.6-i2 \( \bigl[0\) , \( i\) , \( 0\) , \( -180 i - 19\) , \( -769 i + 655\bigr] \)
67600.6-i3 \( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( -701 i - 447\) , \( 61718 i - 76839\bigr] \)
67600.6-i4 \( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( 64 i + 83\) , \( 415 i - 320\bigr] \)
67600.6-i5 \( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( -441 i - 57\) , \( 2338 i - 2941\bigr] \)
67600.6-i6 \( \bigl[0\) , \( i\) , \( 0\) , \( 980 i - 99\) , \( -4137 i - 861\bigr] \)
67600.6-i7 \( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( -2276 i - 47\) , \( 31083 i - 27144\bigr] \)
67600.6-i8 \( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( -36331 i - 787\) , \( 1957246 i - 1804685\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph