Elliptic curve isogeny class 11.1-a over number field \(\Q(\sqrt{77}) \)

• Base field: \(\Q(\sqrt{77}) \)
• Label: 2.2.77.1-11.1-a
• Conductor: 11.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 11.1-a over \(\Q(\sqrt{77}) \)

Isogeny class 11.1-a contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
11.1-a1	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -70382 a - 273705\) , \( 21156761 a + 82247005\bigr] \)
11.1-a2	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -92 a - 355\) , \( 1671 a + 6495\bigr] \)
11.1-a3	\( \bigl[0\) , \( a + 1\) , \( 1\) , \( -2 a - 5\) , \( -19 a - 75\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph