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

• Base field: \(\Q(\sqrt{77}) \)
• Label: 2.2.77.1-7.1-b
• Conductor: 7.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
7.1-b1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -3 a + 4\) , \( -2 a + 4\bigr] \)
7.1-b2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 2 a - 21\) , \( 26 a - 133\bigr] \)
7.1-b3	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 422 a - 2086\) , \( 11275 a - 55139\bigr] \)
7.1-b4	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 22 a - 131\) , \( 228 a - 1147\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph