Elliptic curve isogeny class 25.1-b over number field \(\Q(\sqrt{29}) \)

• Base field: \(\Q(\sqrt{29}) \)
• Label: 2.2.29.1-25.1-b
• Conductor: 25.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{29}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 7 \); class number \(1\).

Elliptic curves in class 25.1-b over \(\Q(\sqrt{29}) \)

Isogeny class 25.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
25.1-b1	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 12 a - 43\) , \( -36 a + 111\bigr] \)
25.1-b2	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 7 a - 28\) , \( -69 a + 216\bigr] \)
25.1-b3	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -73 a + 217\) , \( 1763 a - 5657\bigr] \)
25.1-b4	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 57 a - 198\) , \( 397 a - 1296\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 6 & 3 \\ 2 & 1 & 3 & 6 \\ 6 & 3 & 1 & 2 \\ 3 & 6 & 2 & 1 \end{array}\right)\)

Isogeny graph