Elliptic curve isogeny class 256.1-f over number field \(\Q(\sqrt{29}) \)

• Base field: \(\Q(\sqrt{29}) \)
• Label: 2.2.29.1-256.1-f
• Conductor: 256.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 256.1-f over \(\Q(\sqrt{29}) \)

Isogeny class 256.1-f contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
256.1-f1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 31\) , \( -39 a + 4\bigr] \)
256.1-f2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 209\) , \( 1161 a - 476\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph