Elliptic curve isogeny class 18.1-d over number field 4.4.15952.1

• Base field: 4.4.15952.1
• Label: 4.4.15952.1-18.1-d
• Conductor: 18.1
• Rank: \( 0 \)

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-d over 4.4.15952.1

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

Curve label	Weierstrass Coefficients
18.1-d1	\( \bigl[a^{2} - a - 3\) , \( 0\) , \( -a^{3} + a^{2} + 6 a - 1\) , \( 8 a^{3} - 18 a^{2} - 30 a + 58\) , \( -80 a^{3} + 26 a^{2} + 502 a - 104\bigr] \)
18.1-d2	\( \bigl[-a^{3} + a^{2} + 5 a - 2\) , \( a^{3} - 5 a - 2\) , \( a\) , \( 2 a^{3} - 3 a^{2} - 8 a + 6\) , \( 3 a^{3} - 4 a^{2} - 11 a + 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph