Elliptic curve isogeny class 7.1-a over number field \(\Q(\sqrt{77}) \)

• Base field: \(\Q(\sqrt{77}) \)
• Label: 2.2.77.1-7.1-a
• Conductor: 7.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 7.1-a over \(\Q(\sqrt{77}) \)

Isogeny class 7.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
7.1-a1	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 116 a - 566\) , \( -1240 a + 6064\bigr] \)
7.1-a2	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( a - 1\) , \( -2\bigr] \)
7.1-a3	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 6 a - 26\) , \( 28 a - 138\bigr] \)
7.1-a4	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 111 a - 586\) , \( -1218 a + 6134\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph