Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-63.1-a
Conductor 63.1
Rank \( 0 \)

Related objects

Learn more about

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

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

Elliptic curves in class 63.1-a over \(\Q(\sqrt{-7}) \)

Isogeny class 63.1-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
63.1-a1 \( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \)
63.1-a2 \( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)
63.1-a3 \( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \)
63.1-a4 \( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \)
63.1-a5 \( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( a - 1\) , \( -a\bigr] \)
63.1-a6 \( \bigl[1\) , \( a\) , \( a\) , \( -2 a + 1\) , \( 0\bigr] \)
63.1-a7 \( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \)
63.1-a8 \( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 8 & 4 & 8 & 16 & 16 & 2 & 4 \\ 8 & 1 & 2 & 4 & 2 & 2 & 4 & 8 \\ 4 & 2 & 1 & 2 & 4 & 4 & 2 & 4 \\ 8 & 4 & 2 & 1 & 8 & 8 & 4 & 8 \\ 16 & 2 & 4 & 8 & 1 & 4 & 8 & 16 \\ 16 & 2 & 4 & 8 & 4 & 1 & 8 & 16 \\ 2 & 4 & 2 & 4 & 8 & 8 & 1 & 2 \\ 4 & 8 & 4 & 8 & 16 & 16 & 2 & 1 \end{array}\right)\)

Isogeny graph