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

• Base field: \(\Q(\sqrt{77}) \)
• Label: 2.2.77.1-77.1-d
• Conductor: 77.1
• Rank: \( 2 \)

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

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

Elliptic curves in class 77.1-d over \(\Q(\sqrt{77}) \)

Isogeny class 77.1-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
77.1-d1	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 36 a + 137\) , \( -619 a - 2411\bigr] \)
77.1-d2	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 469 a - 2246\) , \( 10656 a - 52022\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph