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

• Base field: \(\Q(\sqrt{77}) \)
• Label: 2.2.77.1-77.1-j
• 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-j over \(\Q(\sqrt{77}) \)

Isogeny class 77.1-j contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
77.1-j1	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -803 a - 3120\) , \( -24422 a - 94941\bigr] \)
77.1-j2	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -443 a - 1720\) , \( -48462 a - 188396\bigr] \)
77.1-j3	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 3967 a + 15430\) , \( 1269148 a + 4933819\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph