Elliptic curve isogeny class 17.2-a over number field 4.4.2624.1

• Base field: 4.4.2624.1
• Label: 4.4.2624.1-17.2-a
• Conductor: 17.2
• Rank: \( 0 \)

Base field 4.4.2624.1

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

Elliptic curves in class 17.2-a over 4.4.2624.1

Isogeny class 17.2-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
17.2-a1	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 5 a^{3} - 20 a^{2} + 6 a - 5\) , \( 3 a^{3} - 79 a^{2} + 16 a + 15\bigr] \)
17.2-a2	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 6 a - 5\) , \( a^{3} + 3 a^{2} - 7 a + 3\bigr] \)
17.2-a3	\( \bigl[a\) , \( a + 1\) , \( a\) , \( a\) , \( 0\bigr] \)
17.2-a4	\( \bigl[1\) , \( a^{3} - 3 a^{2} - a + 2\) , \( a^{2} - 2 a\) , \( 52 a^{3} - 116 a^{2} - 123 a + 123\) , \( 66 a^{3} - 144 a^{2} - 158 a + 136\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph