Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-76050.5-d
Conductor 76050.5
Rank \( 0 \)

Related objects

Learn more

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

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

Elliptic curves in class 76050.5-d over \(\Q(\sqrt{-1}) \)

Isogeny class 76050.5-d contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
76050.5-d1 \( \bigl[1\) , \( 0\) , \( i\) , \( 407 i + 244\) , \( 129 i - 3963\bigr] \)
76050.5-d2 \( \bigl[1\) , \( 0\) , \( i\) , \( -52423 i - 35581\) , \( 6098960 i + 666080\bigr] \)
76050.5-d3 \( \bigl[i\) , \( 0\) , \( 1\) , \( -29803 i + 3759\) , \( 1091984 i - 1705272\bigr] \)
76050.5-d4 \( \bigl[i\) , \( 0\) , \( 1\) , \( 572 i + 2949\) , \( 63041 i - 16017\bigr] \)
76050.5-d5 \( \bigl[1\) , \( 0\) , \( i\) , \( -298 i - 1741\) , \( 5735 i - 31891\bigr] \)
76050.5-d6 \( \bigl[i\) , \( 0\) , \( 1\) , \( 377 i + 284\) , \( 745 i + 4081\bigr] \)
76050.5-d7 \( \bigl[1\) , \( 0\) , \( i\) , \( 1007 i - 71\) , \( 11736 i + 1812\bigr] \)
76050.5-d8 \( \bigl[i\) , \( 0\) , \( 1\) , \( -3673 i - 1831\) , \( -86960 i - 37580\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph