Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-88200.2-m
Conductor 88200.2
Rank \( 1 \)

Related objects

Learn more about

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

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

Elliptic curves in class 88200.2-m over \(\Q(\sqrt{-1}) \)

Isogeny class 88200.2-m contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
88200.2-m1 \( \bigl[0\) , \( 1\) , \( 0\) , \( -15\) , \( 90\bigr] \)
88200.2-m2 \( \bigl[i + 1\) , \( -i\) , \( 0\) , \( -600\) , \( 300 i\bigr] \)
88200.2-m3 \( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 150\) , \( 0\bigr] \)
88200.2-m4 \( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 1620\) , \( -25284 i\bigr] \)
88200.2-m5 \( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 105\) , \( 396 i\bigr] \)
88200.2-m6 \( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 1680\) , \( 26226 i\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph