Elliptic curve isogeny class 29.1-b over number field 4.4.5125.1

• Base field: 4.4.5125.1
• Label: 4.4.5125.1-29.1-b
• Conductor: 29.1
• Rank: \( 1 \)

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-b over 4.4.5125.1

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

Curve label	Weierstrass Coefficients
29.1-b1	\( \bigl[a^{3} - 5 a - 4\) , \( -a^{3} + 4 a + 4\) , \( a + 1\) , \( -1238 a^{3} - 283 a^{2} + 6707 a + 6118\) , \( 9222 a^{3} - 1273 a^{2} - 59782 a - 52486\bigr] \)
29.1-b2	\( \bigl[a^{2} - a - 3\) , \( a^{3} - 2 a^{2} - 3 a + 3\) , \( a^{3} - a^{2} - 3 a\) , \( -3 a^{3} + 7 a^{2} + 8 a - 18\) , \( 4 a^{3} - 14 a^{2} - 9 a + 43\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph