Elliptic curve isogeny class 18.1-c over number field 4.4.15952.1

• Base field: 4.4.15952.1
• Label: 4.4.15952.1-18.1-c
• 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-c over 4.4.15952.1

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

Curve label	Weierstrass Coefficients
18.1-c1	\( \bigl[a^{3} - 6 a\) , \( -a\) , \( -a^{3} + a^{2} + 6 a - 2\) , \( -42 a^{3} + 16 a^{2} + 265 a - 73\) , \( 212 a^{3} - 87 a^{2} - 1322 a + 361\bigr] \)
18.1-c2	\( \bigl[a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - 5 a - 1\) , \( a^{3} - 9 a + 3\) , \( -a^{3} + a^{2} + 2 a - 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph