Elliptic curve isogeny class 22.1-b over number field 4.4.16448.1

• Base field: 4.4.16448.1
• Label: 4.4.16448.1-22.1-b
• Conductor: 22.1
• Rank: \( 0 \)

Base field 4.4.16448.1

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

Elliptic curves in class 22.1-b over 4.4.16448.1

Isogeny class 22.1-b contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
22.1-b1	\( \bigl[2 a^{3} - 5 a^{2} - 8 a + 1\) , \( a^{2} - 3 a - 2\) , \( a + 1\) , \( -3 a^{3} + 10 a^{2} + 3 a\) , \( -3 a^{3} + 11 a^{2} + a - 4\bigr] \)
22.1-b2	\( \bigl[2 a^{3} - 5 a^{2} - 8 a + 1\) , \( a^{2} - 3 a - 2\) , \( a + 1\) , \( 7 a^{3} - 50 a^{2} - 2 a + 20\) , \( 90 a^{3} - 478 a^{2} - 107 a + 190\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph