Elliptic curve isogeny class 77.1-a over number field \(\Q(\sqrt{77}) \)

• Base field: \(\Q(\sqrt{77}) \)
• Label: 2.2.77.1-77.1-a
• Conductor: 77.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 77.1-a over \(\Q(\sqrt{77}) \)

Isogeny class 77.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
77.1-a1	\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 7 a + 15\) , \( 4 a + 52\bigr] \)
77.1-a2	\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 42 a - 155\) , \( 228 a - 1038\bigr] \)
77.1-a3	\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 592 a - 2850\) , \( 15694 a - 76652\bigr] \)
77.1-a4	\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 12 a - 15\) , \( 20 a - 44\bigr] \)

Rank

Rank: \( 1 \)

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