Elliptic curve isogeny class 18.1-b over number field 4.4.15952.1

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

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

Curve label	Weierstrass Coefficients
18.1-b1	\( \bigl[-a^{3} + a^{2} + 6 a - 1\) , \( -a^{3} + a^{2} + 6 a - 1\) , \( a^{2} - 2\) , \( -8 a^{3} + 18 a^{2} + 13 a - 4\) , \( -25 a^{3} + 57 a^{2} + 29 a - 12\bigr] \)
18.1-b2	\( \bigl[a\) , \( -2 a^{3} + a^{2} + 10 a - 1\) , \( a^{2} - 3\) , \( a^{3} - 6 a^{2} - 2 a + 14\) , \( 115 a^{3} + 16 a^{2} - 651 a - 403\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph