Elliptic curve isogeny class 25.2-a over number field \(\Q(\sqrt{29}) \)

• Base field: \(\Q(\sqrt{29}) \)
• Label: 2.2.29.1-25.2-a
• Conductor: 25.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 25.2-a over \(\Q(\sqrt{29}) \)

Isogeny class 25.2-a contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
25.2-a1	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -16 a - 38\) , \( -64 a - 195\bigr] \)
25.2-a2	\( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( -a + 2\) , \( -a - 2\bigr] \)
25.2-a3	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -15 a - 40\) , \( -481 a - 1066\bigr] \)
25.2-a4	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 0\) , \( 17 a + 37\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 5 & 15 \\ 3 & 1 & 15 & 5 \\ 5 & 15 & 1 & 3 \\ 15 & 5 & 3 & 1 \end{array}\right)\)

Isogeny graph