Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-180.4-a
Conductor 180.4
Rank \( 0 \)

Related objects

Learn more about

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

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

Elliptic curves in class 180.4-a over \(\Q(\sqrt{-11}) \)

Isogeny class 180.4-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
180.4-a1 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 30 a - 277\) , \( -348 a + 1685\bigr] \)
180.4-a2 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -30 a - 77\) , \( -204 a - 199\bigr] \)
180.4-a3 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 3\) , \( 3\bigr] \)
180.4-a4 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -17\) , \( -12 a + 23\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 4 & 2 \\ 4 & 1 & 4 & 2 \\ 4 & 4 & 1 & 2 \\ 2 & 2 & 2 & 1 \end{array}\right)\)

Isogeny graph