Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-27648.2-n
Conductor 27648.2
Rank \( 0 \)

Related objects

Learn more

Base field \(\Q(\sqrt{-2}) \)

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

Elliptic curves in class 27648.2-n over \(\Q(\sqrt{-2}) \)

Isogeny class 27648.2-n contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
27648.2-n1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 470 a - 37\) , \( 3705 a + 3939\bigr] \)
27648.2-n2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 382 a - 389\) , \( -4615 a + 611\bigr] \)
27648.2-n3 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 10 a + 13\) , \( 17 a - 31\bigr] \)
27648.2-n4 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2 a - 19\) , \( -3 a - 39\bigr] \)
27648.2-n5 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 22 a - 29\) , \( -79 a - 37\bigr] \)
27648.2-n6 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 30 a + 3\) , \( 81 a + 27\bigr] \)
27648.2-n7 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -90 a - 117\) , \( 393 a + 627\bigr] \)
27648.2-n8 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -18 a + 171\) , \( -567 a + 243\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 12 & 4 & 12 & 6 & 2 & 4 & 3 \\ 12 & 1 & 12 & 4 & 2 & 6 & 3 & 4 \\ 4 & 12 & 1 & 3 & 6 & 2 & 4 & 12 \\ 12 & 4 & 3 & 1 & 2 & 6 & 12 & 4 \\ 6 & 2 & 6 & 2 & 1 & 3 & 6 & 2 \\ 2 & 6 & 2 & 6 & 3 & 1 & 2 & 6 \\ 4 & 3 & 4 & 12 & 6 & 2 & 1 & 12 \\ 3 & 4 & 12 & 4 & 2 & 6 & 12 & 1 \end{array}\right)\)

Isogeny graph