Elliptic curve isogeny class 9.1-e over number field 4.4.17428.1

• Base field: 4.4.17428.1
• Label: 4.4.17428.1-9.1-e
• Conductor: 9.1
• Rank: \( 0 \)

Base field 4.4.17428.1

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

Elliptic curves in class 9.1-e over 4.4.17428.1

Isogeny class 9.1-e contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
9.1-e1	\( \bigl[a^{3} + a^{2} - 3 a - 4\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a^{3} + a^{2} - 4 a - 3\) , \( 107 a^{3} + 149 a^{2} - 292 a - 270\) , \( 1713 a^{3} + 2346 a^{2} - 4722 a - 4338\bigr] \)
9.1-e2	\( \bigl[a^{3} - 4 a\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( 1\) , \( -79 a^{3} - 106 a^{2} + 216 a + 198\) , \( 554 a^{3} + 760 a^{2} - 1529 a - 1406\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph