Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-19600.3-b
Conductor 19600.3
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 19600.3-b over \(\Q(\sqrt{-1}) \)

Isogeny class 19600.3-b contains 6 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
19600.3-b1 \( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 2728 i - 2046\) , \( 76890 i - 13980\bigr] \)
19600.3-b2 \( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 8 i - 6\) , \( -22 i + 4\bigr] \)
19600.3-b3 \( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( -72 i + 54\) , \( 506 i - 92\bigr] \)
19600.3-b4 \( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 568 i - 426\) , \( 6138 i - 1116\bigr] \)
19600.3-b5 \( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 168 i - 126\) , \( -1078 i + 196\bigr] \)
19600.3-b6 \( \bigl[i + 1\) , \( -i + 1\) , \( 0\) , \( 43688 i - 32766\) , \( 4852826 i - 882332\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph