Elliptic curve isogeny class 29.1-a over number field 4.4.5125.1

• Base field: 4.4.5125.1
• Label: 4.4.5125.1-29.1-a
• Conductor: 29.1
• 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 29.1-a over 4.4.5125.1

Isogeny class 29.1-a contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
29.1-a1	\( \bigl[a^{3} - 4 a - 4\) , \( -a - 1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -64 a^{3} + 32 a^{2} + 393 a - 43\) , \( 43 a^{3} - 491 a^{2} - 169 a + 3203\bigr] \)
29.1-a2	\( \bigl[a^{3} - a^{2} - 4 a + 1\) , \( 0\) , \( a^{3} - 4 a - 4\) , \( a^{3} - a^{2} - 6 a - 2\) , \( a^{3} - 7 a - 7\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph