Elliptic curve isogeny class 196.1-b over number field \(\Q(\sqrt{77}) \)

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

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

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

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

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

Curve label	Weierstrass Coefficients
196.1-b1	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -1194 a - 4779\) , \( -50124 a - 194381\bigr] \)
196.1-b2	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -4 a - 19\) , \( 10 a + 37\bigr] \)
196.1-b3	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 31 a + 121\) , \( -291 a - 1125\bigr] \)
196.1-b4	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -249 a - 999\) , \( -4155 a - 16133\bigr] \)
196.1-b5	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -74 a - 299\) , \( 612 a + 2361\bigr] \)
196.1-b6	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -19114 a - 76459\) , \( -3107276 a - 12043085\bigr] \)

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