Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-50625.3-e
Conductor 50625.3
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 50625.3-e over \(\Q(\sqrt{-1}) \)

Isogeny class 50625.3-e contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
50625.3-e1 \( \bigl[i + 1\) , \( i\) , \( i\) , \( -38 i + 281\) , \( -1672 i - 356\bigr] \)
50625.3-e2 \( \bigl[i + 1\) , \( i\) , \( 1\) , \( 337 i + 2530\) , \( -47672 i + 9956\bigr] \)
50625.3-e3 \( \bigl[i + 1\) , \( i\) , \( i\) , \( 337 i - 844\) , \( -10547 i - 1856\bigr] \)
50625.3-e4 \( \bigl[i + 1\) , \( i\) , \( 1\) , \( -38 i - 95\) , \( -422 i + 81\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 3 & 2 \\ 6 & 1 & 2 & 3 \\ 3 & 2 & 1 & 6 \\ 2 & 3 & 6 & 1 \end{array}\right)\)

Isogeny graph