Elliptic curve isogeny class 21.1-b over number field 4.4.19429.1

• Base field: 4.4.19429.1
• Label: 4.4.19429.1-21.1-b
• Conductor: 21.1
• Rank: \( 0 \)

Base field 4.4.19429.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 7 x^{2} - x + 5 \); class number \(1\).

Elliptic curves in class 21.1-b over 4.4.19429.1

Isogeny class 21.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
21.1-b1	\( \bigl[a^{2} - 3\) , \( a^{2} - 4\) , \( a^{3} - 2 a^{2} - 4 a + 3\) , \( a^{3} + 3 a^{2} + 9 a + 12\) , \( 95 a^{3} - 11 a^{2} - 654 a - 604\bigr] \)
21.1-b2	\( \bigl[a^{3} - 2 a^{2} - 4 a + 3\) , \( a^{3} - 3 a^{2} - 4 a + 6\) , \( a^{3} - 2 a^{2} - 3 a + 2\) , \( -3 a^{3} + 9 a^{2} + 16 a - 18\) , \( -15 a^{3} - 44 a^{2} - 8 a + 36\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph