Elliptic curve isogeny class 99.1-d over number field \(\Q(\sqrt{77}) \)

• Base field: \(\Q(\sqrt{77}) \)
• Label: 2.2.77.1-99.1-d
• Conductor: 99.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 99.1-d over \(\Q(\sqrt{77}) \)

Isogeny class 99.1-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
99.1-d1	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 96 a + 381\) , \( -746 a - 2880\bigr] \)
99.1-d2	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -509 a - 2039\) , \( -9095 a - 35308\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph