Elliptic curve isogeny class 25.1-a over number field \(\Q(\sqrt{69}) \)

• Base field: \(\Q(\sqrt{69}) \)
• Label: 2.2.69.1-25.1-a
• Conductor: 25.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{69}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 17 \); class number \(1\).

Elliptic curves in class 25.1-a over \(\Q(\sqrt{69}) \)

Isogeny class 25.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
25.1-a1	\( \bigl[0\) , \( 1\) , \( 1\) , \( -232 a - 847\) , \( 3842 a + 14036\bigr] \)
25.1-a2	\( \bigl[0\) , \( 1\) , \( 1\) , \( -2 a - 7\) , \( 8 a + 29\bigr] \)
25.1-a3	\( \bigl[0\) , \( 1\) , \( 1\) , \( 18 a + 63\) , \( -200 a - 734\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph