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

• Base field: \(\Q(\sqrt{77}) \)
• Label: 2.2.77.1-49.1-a
• 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-a over \(\Q(\sqrt{77}) \)

Isogeny class 49.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
49.1-a1	\( \bigl[a\) , \( 1\) , \( 0\) , \( 72 a - 520\) , \( 1215 a - 5391\bigr] \)
49.1-a2	\( \bigl[a\) , \( 1\) , \( 0\) , \( 2 a + 5\) , \( 4 a - 8\bigr] \)
49.1-a3	\( \bigl[a\) , \( 1\) , \( 0\) , \( 2 a - 30\) , \( -3 a + 27\bigr] \)
49.1-a4	\( \bigl[a\) , \( 1\) , \( 0\) , \( -243 a - 1745\) , \( 7396 a + 18647\bigr] \)

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