Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-12544.1-e
Conductor 12544.1
Rank not recorded

Related objects

Learn more about

Base field \(\Q(\sqrt{-1}) \)

Generator \(i\), with minimal polynomial \( x^{2} + 1 \); class number \(1\).

Elliptic curves in class 12544.1-e over \(\Q(\sqrt{-1}) \)

Isogeny class 12544.1-e contains 6 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
12544.1-e1 \( \bigl[0\) , \( i\) , \( 0\) , \( 2728\) , \( 55920 i\bigr] \)
12544.1-e2 \( \bigl[0\) , \( i\) , \( 0\) , \( 8\) , \( -16 i\bigr] \)
12544.1-e3 \( \bigl[0\) , \( i\) , \( 0\) , \( -72\) , \( 368 i\bigr] \)
12544.1-e4 \( \bigl[0\) , \( i\) , \( 0\) , \( 568\) , \( 4464 i\bigr] \)
12544.1-e5 \( \bigl[0\) , \( i\) , \( 0\) , \( 168\) , \( -784 i\bigr] \)
12544.1-e6 \( \bigl[0\) , \( i\) , \( 0\) , \( 43688\) , \( 3529328 i\bigr] \)

Rank

Rank not yet determined.

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