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

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

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

Curve label	Weierstrass Coefficients
49.1-b1	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -1657 a - 6449\) , \( -73928 a - 287391\bigr] \)
49.1-b2	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -12 a - 44\) , \( -162 a - 629\bigr] \)
49.1-b3	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -327 a - 1269\) , \( -6140 a - 23869\bigr] \)
49.1-b4	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 7276 a - 35531\) , \( -707728 a + 3458853\bigr] \)

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