Elliptic curve isogeny class 23.2-a over number field \(\Q(\sqrt{77}) \)

• Base field: \(\Q(\sqrt{77}) \)
• Label: 2.2.77.1-23.2-a
• Conductor: 23.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 23.2-a over \(\Q(\sqrt{77}) \)

Isogeny class 23.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
23.2-a1	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( a - 3\) , \( -12 a + 51\bigr] \)
23.2-a2	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 56 a - 273\) , \( -394 a + 1920\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph