Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-5625.3-b
Conductor 5625.3
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 5625.3-b over \(\Q(\sqrt{-1}) \)

Isogeny class 5625.3-b contains 10 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
5625.3-b1 \( \bigl[1\) , \( 0\) , \( 1\) , \( -2625 i + 9874\) , \( -367500 i - 151477\bigr] \)
5625.3-b2 \( \bigl[i\) , \( 0\) , \( i\) , \( 2625 i + 9875\) , \( -367500 i + 151477\bigr] \)
5625.3-b3 \( \bigl[1\) , \( 0\) , \( 1\) , \( -2751\) , \( -104477\bigr] \)
5625.3-b4 \( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 23\bigr] \)
5625.3-b5 \( \bigl[i\) , \( 0\) , \( i\) , \( 875\) , \( 5227\bigr] \)
5625.3-b6 \( \bigl[1\) , \( 0\) , \( 1\) , \( -251\) , \( -727\bigr] \)
5625.3-b7 \( \bigl[i\) , \( 0\) , \( i\) , \( -125\) , \( -523\bigr] \)
5625.3-b8 \( \bigl[1\) , \( 0\) , \( 1\) , \( -3376\) , \( -75727\bigr] \)
5625.3-b9 \( \bigl[i\) , \( 0\) , \( i\) , \( -2000\) , \( -34273\bigr] \)
5625.3-b10 \( \bigl[1\) , \( 0\) , \( 1\) , \( -54001\) , \( -4834477\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph