Elliptic curve isogeny class 18.1-a over number field 4.4.15952.1

• Base field: 4.4.15952.1
• Label: 4.4.15952.1-18.1-a
• Conductor: 18.1
• Rank: \( 1 \)

Base field 4.4.15952.1

Generator \(a\), with minimal polynomial \( x^{4} - 6 x^{2} - 2 x + 1 \); class number \(1\).

Elliptic curves in class 18.1-a over 4.4.15952.1

Isogeny class 18.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
18.1-a1	\( \bigl[-a^{3} + a^{2} + 6 a - 1\) , \( a + 1\) , \( a^{3} - 6 a - 1\) , \( 35 a^{3} + 6 a^{2} - 209 a - 114\) , \( -163 a^{3} - 45 a^{2} + 967 a + 595\bigr] \)
18.1-a2	\( \bigl[a^{3} - 6 a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a + 1\) , \( 115 a^{3} - 71 a^{2} - 643 a + 184\) , \( 1804 a^{3} - 1140 a^{2} - 10073 a + 2822\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph