Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-88200.2-l
Conductor 88200.2
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 88200.2-l over \(\Q(\sqrt{-1}) \)

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

Curve label Weierstrass Coefficients
88200.2-l1 \( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i - 60\) , \( 511 i\bigr] \)
88200.2-l2 \( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i - 280\) , \( -4043 i\bigr] \)
88200.2-l3 \( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 170\) , \( -713 i\bigr] \)
88200.2-l4 \( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 45\) , \( 112 i\bigr] \)
88200.2-l5 \( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 2620\) , \( -51183 i\bigr] \)
88200.2-l6 \( \bigl[0\) , \( -1\) , \( 0\) , \( -175\) , \( 952\bigr] \)

Rank

Rank: \( 1 \)

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