Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-82369.3-b
Conductor 82369.3
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 82369.3-b over \(\Q(\sqrt{-1}) \)

Isogeny class 82369.3-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
82369.3-b1 \( \bigl[i\) , \( 1\) , \( 0\) , \( 57 i - 8\) , \( 1917 i - 3083\bigr] \)
82369.3-b2 \( \bigl[1\) , \( -1\) , \( 0\) , \( 102 i - 208\) , \( -880 i + 1089\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph