Elliptic curve isogeny class 7.2-b over number field 4.4.16317.1

• Base field: 4.4.16317.1
• Label: 4.4.16317.1-7.2-b
• 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-b over 4.4.16317.1

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

Curve label	Weierstrass Coefficients
7.2-b1	\( \bigl[a\) , \( a^{3} - 6 a - 3\) , \( 0\) , \( -22 a^{3} + 64 a - 25\) , \( -110 a^{3} - 67 a^{2} + 242 a - 20\bigr] \)
7.2-b2	\( \bigl[a\) , \( a^{3} - 6 a - 3\) , \( 0\) , \( -7 a^{3} + 24 a + 5\) , \( 12 a^{3} + 4 a^{2} - 33 a - 6\bigr] \)
7.2-b3	\( \bigl[1\) , \( a\) , \( a^{3} - a^{2} - 4 a + 1\) , \( -31 a^{3} + 50 a^{2} + 110 a - 146\) , \( -1418 a^{3} + 3139 a^{2} + 5136 a - 8086\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph