Elliptic curve isogeny class 81.1-a over number field \(\Q(\sqrt{29}) \)

• Base field: \(\Q(\sqrt{29}) \)
• Label: 2.2.29.1-81.1-a
• Conductor: 81.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 81.1-a over \(\Q(\sqrt{29}) \)

Isogeny class 81.1-a contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
81.1-a1	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -229 a - 503\) , \( 3200 a + 7022\bigr] \)
81.1-a2	\( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -4 a - 8\) , \( 5 a + 11\bigr] \)
81.1-a3	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 229 a - 725\) , \( -2972 a + 9498\bigr] \)
81.1-a4	\( \bigl[a + 1\) , \( 1\) , \( 1\) , \( 4 a - 5\) , \( -2 a + 12\bigr] \)

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