Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-27225.5-c
Conductor 27225.5
Rank \( 1 \)

Related objects

Learn more

Base field \(\Q(\sqrt{-11}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 3 \); class number \(1\).

Elliptic curves in class 27225.5-c over \(\Q(\sqrt{-11}) \)

Isogeny class 27225.5-c contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
27225.5-c1 \( \bigl[1\) , \( 1\) , \( a\) , \( -226 a - 211\) , \( 2362 a - 119\bigr] \)
27225.5-c2 \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 926 a - 240\) , \( 8066 a + 15261\bigr] \)
27225.5-c3 \( \bigl[1\) , \( 1\) , \( a\) , \( -6 a - 5986\) , \( 349 a - 182378\bigr] \)
27225.5-c4 \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 46 a - 75\) , \( -30 a + 741\bigr] \)
27225.5-c5 \( \bigl[1\) , \( 1\) , \( a\) , \( -171 a - 376\) , \( 2725 a - 3287\bigr] \)
27225.5-c6 \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 1091 a + 750\) , \( 21992 a - 19983\bigr] \)
27225.5-c7 \( \bigl[1\) , \( 1\) , \( a\) , \( 544 a + 2594\) , \( 27233 a - 23648\bigr] \)
27225.5-c8 \( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 14841 a - 3870\) , \( 496664 a + 1012785\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph