Elliptic curve isogeny class 22.1-b over number field 4.4.17609.1

• Base field: 4.4.17609.1
• Label: 4.4.17609.1-22.1-b
• Conductor: 22.1
• Rank: \( 0 \)

Base field 4.4.17609.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 7 x^{2} + 10 x - 1 \); class number \(1\).

Elliptic curves in class 22.1-b over 4.4.17609.1

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

Curve label	Weierstrass Coefficients
22.1-b1	\( \bigl[2 a^{3} + a^{2} - 10 a + 2\) , \( a^{3} - 5 a + 2\) , \( 0\) , \( 35 a^{3} + 22 a^{2} - 207 a + 23\) , \( 364 a^{3} + 184 a^{2} - 2266 a + 243\bigr] \)
22.1-b2	\( \bigl[2 a^{3} + a^{2} - 10 a + 2\) , \( a^{3} - 5 a + 2\) , \( 0\) , \( 25415 a^{3} + 12302 a^{2} - 159652 a + 17118\) , \( 3260309 a^{3} + 1582114 a^{2} - 20472503 a + 2195029\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph