Properties

Base field \(\Q(\sqrt{77}) \)
Label 2.2.77.1-1.1-a
Conductor 1.1
Rank not recorded

Related objects

Learn more about

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

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

Elliptic curves in class 1.1-a over \(\Q(\sqrt{77}) \)

Isogeny class 1.1-a contains 4 curves linked by isogenies of degrees dividing 14.

Curve label Weierstrass Coefficients
1.1-a1 \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -2 a + 7\) , \( -a + 7\bigr] \)
1.1-a2 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 2 a + 4\) , \( 3 a + 10\bigr] \)
1.1-a3 \( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -7 a - 13\) , \( 13 a + 60\bigr] \)
1.1-a4 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 7 a - 21\) , \( -6 a + 52\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 7 & 2 & 14 \\ 7 & 1 & 14 & 2 \\ 2 & 14 & 1 & 7 \\ 14 & 2 & 7 & 1 \end{array}\right)\)

Isogeny graph