Elliptic curve isogeny class 22.1-a over number field 3.3.316.1

• Base field: 3.3.316.1
• Label: 3.3.316.1-22.1-a
• Conductor: 22.1
• Rank: \( 0 \)

Base field 3.3.316.1

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

Elliptic curves in class 22.1-a over 3.3.316.1

Isogeny class 22.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
22.1-a1	\( \bigl[a^{2} + a - 3\) , \( a^{2} + a - 4\) , \( 1\) , \( 12 a^{2} - 38\) , \( 33 a^{2} - 10 a - 127\bigr] \)
22.1-a2	\( \bigl[1\) , \( a^{2} - a - 2\) , \( 1\) , \( 177 a^{2} - 284 a - 1094\) , \( 821 a^{2} - 2362 a - 6983\bigr] \)
22.1-a3	\( \bigl[1\) , \( a - 1\) , \( a\) , \( 3 a^{2} + 37 a - 20\) , \( 128 a^{2} + 21 a - 39\bigr] \)
22.1-a4	\( \bigl[1\) , \( a - 1\) , \( a\) , \( -7 a^{2} - 8 a + 5\) , \( 13 a^{2} + 15 a - 10\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 4 & 2 \\ 4 & 1 & 4 & 2 \\ 4 & 4 & 1 & 2 \\ 2 & 2 & 2 & 1 \end{array}\right)\)

Isogeny graph