Elliptic curve isogeny class 49.2-d over number field \(\Q(\sqrt{29}) \)

• Base field: \(\Q(\sqrt{29}) \)
• Label: 2.2.29.1-49.2-d
• Conductor: 49.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 49.2-d over \(\Q(\sqrt{29}) \)

Isogeny class 49.2-d contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
49.2-d1	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 26 a - 103\) , \( 137 a - 493\bigr] \)
49.2-d2	\( \bigl[a\) , \( -a\) , \( 0\) , \( 10 a + 21\) , \( 0\bigr] \)
49.2-d3	\( \bigl[a\) , \( -a\) , \( 0\) , \( -40 a - 84\) , \( 23 a + 63\bigr] \)
49.2-d4	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -24 a - 208\) , \( -260 a - 1410\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph