Elliptic curve isogeny class 8.4-a over number field 4.4.15188.1

• Base field: 4.4.15188.1
• Label: 4.4.15188.1-8.4-a
• Conductor: 8.4
• Rank: \( 0 \)

Base field 4.4.15188.1

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

Elliptic curves in class 8.4-a over 4.4.15188.1

Isogeny class 8.4-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
8.4-a1	\( \bigl[\frac{1}{2} a^{3} - \frac{7}{2} a - 1\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a - 3\) , \( a^{3} - a^{2} - 5 a\) , \( \frac{25}{2} a^{3} - 14 a^{2} - \frac{131}{2} a - 27\) , \( -50 a^{3} + 69 a^{2} + 236 a + 92\bigr] \)
8.4-a2	\( \bigl[0\) , \( -a^{2} + a + 3\) , \( a^{3} - a^{2} - 5 a\) , \( -21 a^{3} - 64 a^{2} + 15 a + 22\) , \( \frac{657}{2} a^{3} + 798 a^{2} - \frac{375}{2} a - 246\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph