Elliptic curve isogeny class 41.4-a over number field 6.6.1229312.1

• Base field: 6.6.1229312.1
• Label: 6.6.1229312.1-41.4-a
• Conductor: 41.4
• Rank: \( 2 \)

Base field 6.6.1229312.1

Generator \(a\), with minimal polynomial \( x^{6} - 10 x^{4} + 24 x^{2} - 8 \); class number \(1\).

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 41.4-a over 6.6.1229312.1

Isogeny class 41.4-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
41.4-a1	\( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( -\frac{1}{4} a^{5} - \frac{1}{4} a^{4} + \frac{3}{2} a^{3} + \frac{3}{2} a^{2} - a\) , \( \frac{1}{4} a^{5} + \frac{1}{4} a^{4} - 2 a^{3} - \frac{3}{2} a^{2} + 4 a + 2\) , \( -\frac{1}{4} a^{5} + a^{3} + 1\) , \( \frac{3}{4} a^{4} + a^{3} - 2 a^{2} - 3 a - 1\bigr] \)
41.4-a2	\( \bigl[\frac{1}{4} a^{5} - 2 a^{3} + 4 a\) , \( \frac{1}{4} a^{5} - 2 a^{3} + \frac{1}{2} a^{2} + 3 a - 2\) , \( \frac{1}{4} a^{4} - \frac{3}{2} a^{2} + a + 2\) , \( \frac{3}{4} a^{5} + \frac{3}{4} a^{4} - \frac{15}{2} a^{3} - \frac{13}{2} a^{2} + 16 a + 13\) , \( -\frac{1}{2} a^{5} - \frac{1}{4} a^{4} + \frac{9}{2} a^{3} + \frac{5}{2} a^{2} - 9 a - 6\bigr] \)