Elliptic curve isogeny class 49.1-d over number field \(\Q(\sqrt{77}) \)

• Base field: \(\Q(\sqrt{77}) \)
• Label: 2.2.77.1-49.1-d
• Conductor: 49.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 49.1-d over \(\Q(\sqrt{77}) \)

Isogeny class 49.1-d contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
49.1-d1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -2\) , \( -1\bigr] \)
49.1-d2	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -18 a - 71\) , \( 62 a + 240\bigr] \)
49.1-d3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -37\) , \( -78\bigr] \)
49.1-d4	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -333 a - 1296\) , \( 5907 a + 22962\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 7 & 2 & 14 \\ 7 & 1 & 14 & 2 \\ 2 & 14 & 1 & 7 \\ 14 & 2 & 7 & 1 \end{array}\right)\)

Isogeny graph