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

• Base field: \(\Q(\sqrt{29}) \)
• Label: 2.2.29.1-256.1-d
• 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-d over \(\Q(\sqrt{29}) \)

Isogeny class 256.1-d contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
256.1-d1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a - 73\) , \( 495 a - 1241\bigr] \)
256.1-d2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -2 a + 7\) , \( -17 a + 55\bigr] \)
256.1-d3	\( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a - 75\) , \( 495 a + 746\bigr] \)
256.1-d4	\( \bigl[0\) , \( -a\) , \( 0\) , \( 2 a + 5\) , \( -17 a - 38\bigr] \)

Rank

Rank: \( 1 \)

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