Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-121.1-a
Conductor 121.1
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 121.1-a over \(\Q(\sqrt{-1}) \)

Isogeny class 121.1-a contains 3 curves linked by isogenies of degrees dividing 25.

Curve label Weierstrass Coefficients
121.1-a1 \( \bigl[0\) , \( 1\) , \( i\) , \( -7820\) , \( 263580\bigr] \)
121.1-a2 \( \bigl[0\) , \( 1\) , \( i\) , \( -10\) , \( 20\bigr] \)
121.1-a3 \( \bigl[0\) , \( 1\) , \( i\) , \( 0\) , \( 0\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph