Elliptic curve isogeny class 343.2-c over number field \(\Q(\sqrt{29}) \)

• Base field: \(\Q(\sqrt{29}) \)
• Label: 2.2.29.1-343.2-c
• Conductor: 343.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 343.2-c over \(\Q(\sqrt{29}) \)

Isogeny class 343.2-c contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
343.2-c1	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 63 a - 201\) , \( -444 a + 1415\bigr] \)
343.2-c2	\( \bigl[1\) , \( a\) , \( 1\) , \( 7 a + 6\) , \( 6 a + 7\bigr] \)
343.2-c3	\( \bigl[1\) , \( a\) , \( 1\) , \( -18 a - 39\) , \( -20 a - 79\bigr] \)
343.2-c4	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 38 a - 246\) , \( -415 a + 1624\bigr] \)

Rank

Rank: \( 0 \)

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