Properties

Base field \(\Q(\sqrt{77}) \)
Label 2.2.77.1-196.1-a
Conductor 196.1
Rank \( 0 \)

Related objects

Learn more

Base field \(\Q(\sqrt{77}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 19 \); class number \(1\).

Elliptic curves in class 196.1-a over \(\Q(\sqrt{77}) \)

Isogeny class 196.1-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
196.1-a1 \( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 1192 a - 5972\) , \( 50123 a - 244504\bigr] \)
196.1-a2 \( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 2 a - 22\) , \( -11 a + 48\bigr] \)
196.1-a3 \( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( -33 a + 153\) , \( 290 a - 1415\bigr] \)
196.1-a4 \( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 247 a - 1247\) , \( 4154 a - 20287\bigr] \)
196.1-a5 \( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 72 a - 372\) , \( -613 a + 2974\bigr] \)
196.1-a6 \( \bigl[a + 1\) , \( -a - 1\) , \( a\) , \( 19112 a - 95572\) , \( 3107275 a - 15150360\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph