Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-1800.2-b
Conductor 1800.2
Rank \( 0 \)

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 1800.2-b over \(\Q(\sqrt{-1}) \)

Isogeny class 1800.2-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
1800.2-b1 \( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 20\) , \( 300 i\bigr] \)
1800.2-b2 \( \bigl[i + 1\) , \( 0\) , \( 0\) , \( -20\) , \( -10 i\bigr] \)
1800.2-b3 \( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 5\) , \( 0\bigr] \)
1800.2-b4 \( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 50\) , \( -144 i\bigr] \)
1800.2-b5 \( \bigl[0\) , \( 1\) , \( 0\) , \( -15\) , \( 18\bigr] \)
1800.2-b6 \( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 800\) , \( -8844 i\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph