Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-232.5-a
Conductor 232.5
Rank \( 0 \)

Related objects

Learn more

Base field \(\Q(\sqrt{-7}) \)

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

Elliptic curves in class 232.5-a over \(\Q(\sqrt{-7}) \)

Isogeny class 232.5-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
232.5-a1 \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -6 a + 14\) , \( 13 a + 10\bigr] \)
232.5-a2 \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 19 a + 24\) , \( -34 a + 132\bigr] \)
232.5-a3 \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -a - 1\) , \( -a\bigr] \)
232.5-a4 \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 4 a - 11\) , \( -12 a + 10\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph