Elliptic curve isogeny class 7.2-a over number field 4.4.16317.1

• Base field: 4.4.16317.1
• Label: 4.4.16317.1-7.2-a
• Conductor: 7.2
• Rank: \( 1 \)

Base field 4.4.16317.1

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

Elliptic curves in class 7.2-a over 4.4.16317.1

Isogeny class 7.2-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
7.2-a1	\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( a^{3} - a^{2} - 4 a\) , \( a^{2} - 3\) , \( -111 a^{3} + 277 a^{2} + 364 a - 799\) , \( 1288 a^{3} - 3025 a^{2} - 4436 a + 8320\bigr] \)
7.2-a2	\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( a^{3} - a^{2} - 4 a\) , \( a^{2} - 3\) , \( -a^{3} + 2 a^{2} + 4 a - 4\) , \( -a^{2} + 3\bigr] \)
7.2-a3	\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( a^{3} - a^{2} - 4 a\) , \( a^{2} - 3\) , \( -11 a^{3} - 13 a^{2} + 19 a + 6\) , \( -91 a^{3} - 108 a^{2} + 121 a + 50\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph