Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-61250.3-e
Conductor 61250.3
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 61250.3-e over \(\Q(\sqrt{-1}) \)

Isogeny class 61250.3-e contains 6 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
61250.3-e1 \( \bigl[i\) , \( -1\) , \( i\) , \( -4262\) , \( 109219\bigr] \)
61250.3-e2 \( \bigl[i\) , \( -1\) , \( i\) , \( -12\) , \( -31\bigr] \)
61250.3-e3 \( \bigl[i\) , \( -1\) , \( i\) , \( 113\) , \( 719\bigr] \)
61250.3-e4 \( \bigl[i\) , \( -1\) , \( i\) , \( -887\) , \( 8719\bigr] \)
61250.3-e5 \( \bigl[i\) , \( -1\) , \( i\) , \( -262\) , \( -1531\bigr] \)
61250.3-e6 \( \bigl[i\) , \( -1\) , \( i\) , \( -68262\) , \( 6893219\bigr] \)

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