Elliptic curve isogeny class 29.2-a over number field 4.4.5125.1

• Base field: 4.4.5125.1
• Label: 4.4.5125.1-29.2-a
• Conductor: 29.2
• Rank: \( 0 \)

Base field 4.4.5125.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 6 x^{2} + 7 x + 11 \); class number \(1\).

Elliptic curves in class 29.2-a over 4.4.5125.1

Isogeny class 29.2-a contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
29.2-a1	\( \bigl[a^{3} - 5 a - 3\) , \( -a\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -2 a^{3} + 3 a^{2} + 6 a - 7\) , \( -2 a^{3} + 4 a^{2} + 6 a - 12\bigr] \)
29.2-a2	\( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{3} - 5 a - 3\) , \( 63 a^{3} - 159 a^{2} - 264 a + 319\) , \( -43 a^{3} - 362 a^{2} + 1021 a + 2586\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph