Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-5525.5-b
Conductor 5525.5
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 5525.5-b over \(\Q(\sqrt{-1}) \)

Isogeny class 5525.5-b contains 10 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
5525.5-b1 \( \bigl[i\) , \( 1\) , \( i\) , \( -25680 i + 10614\) , \( 343455 i - 1745489\bigr] \)
5525.5-b2 \( \bigl[i\) , \( 1\) , \( i\) , \( -8295 i - 591\) , \( -229305 i + 183071\bigr] \)
5525.5-b3 \( \bigl[1\) , \( -1\) , \( 1\) , \( -1605 i + 663\) , \( -5065 i + 27149\bigr] \)
5525.5-b4 \( \bigl[i\) , \( 1\) , \( i\) , \( 15 i + 9\) , \( 3 i - 25\bigr] \)
5525.5-b5 \( \bigl[1\) , \( -1\) , \( 1\) , \( 135 i - 112\) , \( -915 i + 251\bigr] \)
5525.5-b6 \( \bigl[1\) , \( -1\) , \( 1\) , \( -1530 i + 713\) , \( -7875 i + 28309\bigr] \)
5525.5-b7 \( \bigl[i\) , \( 1\) , \( i\) , \( 525 i - 501\) , \( -12333 i + 17155\bigr] \)
5525.5-b8 \( \bigl[1\) , \( -1\) , \( 1\) , \( 15 i + 3\) , \( -17 i + 35\bigr] \)
5525.5-b9 \( \bigl[i\) , \( 1\) , \( i\) , \( -105 i + 39\) , \( 15 i - 399\bigr] \)
5525.5-b10 \( \bigl[i\) , \( 1\) , \( i\) , \( -525 i - 26\) , \( -3723 i + 2635\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrr} 1 & 16 & 2 & 16 & 16 & 4 & 16 & 8 & 4 & 8 \\ 16 & 1 & 8 & 16 & 16 & 16 & 4 & 8 & 4 & 2 \\ 2 & 8 & 1 & 8 & 8 & 2 & 8 & 4 & 2 & 4 \\ 16 & 16 & 8 & 1 & 4 & 16 & 16 & 2 & 4 & 8 \\ 16 & 16 & 8 & 4 & 1 & 16 & 16 & 2 & 4 & 8 \\ 4 & 16 & 2 & 16 & 16 & 1 & 16 & 8 & 4 & 8 \\ 16 & 4 & 8 & 16 & 16 & 16 & 1 & 8 & 4 & 2 \\ 8 & 8 & 4 & 2 & 2 & 8 & 8 & 1 & 2 & 4 \\ 4 & 4 & 2 & 4 & 4 & 4 & 4 & 2 & 1 & 2 \\ 8 & 2 & 4 & 8 & 8 & 8 & 2 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph