Elliptic curve isogeny class 464.1-c over number field \(\Q(\sqrt{29}) \)

• Base field: \(\Q(\sqrt{29}) \)
• Label: 2.2.29.1-464.1-c
• Conductor: 464.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 464.1-c over \(\Q(\sqrt{29}) \)

Isogeny class 464.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
464.1-c1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -4\) , \( 24\bigr] \)
464.1-c2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 25 a - 94\) , \( -139 a + 446\bigr] \)
464.1-c3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -9\) , \( 14\bigr] \)
464.1-c4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -25 a - 69\) , \( 139 a + 307\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph