Elliptic curve isogeny class 9.3-a over number field 4.4.17069.1

• Base field: 4.4.17069.1
• Label: 4.4.17069.1-9.3-a
• Conductor: 9.3
• Rank: \( 1 \)

Base field 4.4.17069.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 8 x^{2} - 4 x + 3 \); class number \(1\).

Elliptic curves in class 9.3-a over 4.4.17069.1

Isogeny class 9.3-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
9.3-a1	\( \bigl[a^{2} - 2 a - 4\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( a + 1\) , \( -27 a^{3} - 60 a^{2} - a + 41\) , \( -421 a^{3} - 1057 a^{2} - 357 a + 374\bigr] \)
9.3-a2	\( \bigl[a + 1\) , \( a^{3} - 3 a^{2} - 3 a + 5\) , \( a^{3} - 2 a^{2} - 5 a\) , \( 4 a^{3} - 10 a^{2} - 10 a + 12\) , \( -5 a^{3} - 31 a^{2} - 19 a + 14\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph