Elliptic curve isogeny class 175.6-b over number field \(\Q(\sqrt{29}) \)

• Base field: \(\Q(\sqrt{29}) \)
• Label: 2.2.29.1-175.6-b
• Conductor: 175.6
• Rank: \( 0 \)

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

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

Elliptic curves in class 175.6-b over \(\Q(\sqrt{29}) \)

Isogeny class 175.6-b contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
175.6-b1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -152 a - 335\) , \( 1667 a + 3654\bigr] \)
175.6-b2	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 10 a - 15\) , \( -13 a + 60\bigr] \)
175.6-b3	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 0\) , \( -51 a + 142\bigr] \)
175.6-b4	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 227 a - 735\) , \( 3219 a - 10279\bigr] \)

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