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

• Base field: \(\Q(\sqrt{77}) \)
• Label: 2.2.77.1-7.1-d
• 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-d over \(\Q(\sqrt{77}) \)

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

Curve label	Weierstrass Coefficients
7.1-d1	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -24 a - 109\) , \( -229 a - 919\bigr] \)
7.1-d2	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( a + 1\) , \( a + 2\bigr] \)
7.1-d3	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -4 a - 19\) , \( -27 a - 107\bigr] \)
7.1-d4	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -424 a - 1664\) , \( -11276 a - 43864\bigr] \)

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