Elliptic curve isogeny class 4.1-a over number field 6.6.1767625.1

• Base field: 6.6.1767625.1
• Label: 6.6.1767625.1-4.1-a
• Conductor: 4.1
• Rank: \( 0 \)

Base field 6.6.1767625.1

Generator \(a\), with minimal polynomial \( x^{6} - 7 x^{4} - x^{3} + 11 x^{2} + x - 1 \); class number \(1\).

Elliptic curves in class 4.1-a over 6.6.1767625.1

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

Curve label	Weierstrass Coefficients
4.1-a1	\( \bigl[\frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 3 a^{3} + \frac{5}{2} a^{2} + 4 a - \frac{5}{2}\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 2\) , \( 2 a^{5} - a^{4} - 12 a^{3} + 3 a^{2} + 16 a - 3\) , \( 3 a^{5} - 2 a^{4} - 19 a^{3} + 7 a^{2} + 25 a - 5\) , \( \frac{3}{2} a^{5} + \frac{1}{2} a^{4} - 13 a^{3} - \frac{5}{2} a^{2} + 27 a - \frac{15}{2}\bigr] \)
4.1-a2	\( \bigl[\frac{1}{2} a^{5} - \frac{1}{2} a^{4} - 3 a^{3} + \frac{5}{2} a^{2} + 5 a - \frac{3}{2}\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 7 a\) , \( \frac{3}{2} a^{5} - \frac{1}{2} a^{4} - 9 a^{3} + \frac{3}{2} a^{2} + 11 a - \frac{5}{2}\) , \( -\frac{35}{2} a^{5} + \frac{59}{2} a^{4} + 71 a^{3} - \frac{211}{2} a^{2} - 5 a + \frac{13}{2}\) , \( -60 a^{5} + 101 a^{4} + 252 a^{3} - 368 a^{2} - 47 a + 32\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph