Elliptic curve isogeny class 1.1-a over number field \(\Q(\sqrt{29}) \)

• Base field: \(\Q(\sqrt{29}) \)
• Label: 2.2.29.1-1.1-a
• Conductor: 1.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1.1-a over \(\Q(\sqrt{29}) \)

Isogeny class 1.1-a contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
1.1-a1	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -23 a - 53\) , \( -169 a - 372\bigr] \)
1.1-a2	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 2 a + 2\) , \( a + 1\bigr] \)
1.1-a3	\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 27 a - 74\) , \( 92 a - 284\bigr] \)
1.1-a4	\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 2 a + 6\) , \( 2 a + 4\bigr] \)

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