Elliptic curve isogeny class 4.1-a over number field 4.4.18097.1

• Base field: 4.4.18097.1
• Label: 4.4.18097.1-4.1-a
• Conductor: 4.1
• Rank: \( 1 \)

Base field 4.4.18097.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 7 x^{2} + 6 x + 4 \); class number \(1\).

Elliptic curves in class 4.1-a over 4.4.18097.1

Isogeny class 4.1-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
4.1-a1	\( \bigl[a^{3} - 4 a + 1\) , \( -a + 1\) , \( a^{3} - 4 a\) , \( 2 a^{3} - a^{2} - 14 a - 48\) , \( 38 a^{3} - 31 a^{2} - 170 a - 4\bigr] \)
4.1-a2	\( \bigl[a^{3} - 4 a + 1\) , \( -a + 1\) , \( a^{3} - 4 a\) , \( 2 a^{3} + 4 a^{2} - 9 a - 3\) , \( 4 a^{3} + 8 a^{2} - 15 a - 7\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph