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

• Base field: \(\Q(\sqrt{77}) \)
• Label: 2.2.77.1-77.1-c
• Conductor: 77.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
77.1-c1	\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 5 a - 8\) , \( 10 a - 33\bigr] \)
77.1-c2	\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 55 a - 253\) , \( 466 a - 2263\bigr] \)
77.1-c3	\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -5 a + 37\) , \( 34 a - 157\bigr] \)
77.1-c4	\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 50 a - 293\) , \( 430 a - 2049\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph