Elliptic curve isogeny class 28.1-a over number field \(\Q(\sqrt{77}) \)

• Base field: \(\Q(\sqrt{77}) \)
• Label: 2.2.77.1-28.1-a
• Conductor: 28.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 28.1-a over \(\Q(\sqrt{77}) \)

Isogeny class 28.1-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
28.1-a1	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -1536 a - 5960\) , \( 66830 a + 259805\bigr] \)
28.1-a2	\( \bigl[a\) , \( 0\) , \( 1\) , \( 5 a - 15\) , \( 30 a - 139\bigr] \)
28.1-a3	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 39 a + 165\) , \( 540 a + 2107\bigr] \)
28.1-a4	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -321 a - 1235\) , \( 4940 a + 19211\bigr] \)
28.1-a5	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -96 a - 360\) , \( -1170 a - 4541\bigr] \)
28.1-a6	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -24576 a - 95560\) , \( 4362510 a + 16959197\bigr] \)

Rank

Rank: \( 1 \)

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