Elliptic curve isogeny class 41.2-a over number field 6.6.1229312.1

• Base field: 6.6.1229312.1
• Label: 6.6.1229312.1-41.2-a
• Conductor: 41.2
• Rank: \( 2 \)

Base field 6.6.1229312.1

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

Elliptic curves in class 41.2-a over 6.6.1229312.1

Isogeny class 41.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
41.2-a1	\( \bigl[\frac{1}{4} a^{5} - \frac{3}{2} a^{3}\) , \( -\frac{1}{4} a^{5} - \frac{1}{4} a^{4} + 2 a^{3} + \frac{3}{2} a^{2} - 3 a - 1\) , \( \frac{1}{4} a^{4} + \frac{1}{2} a^{3} - a^{2} - 3 a - 1\) , \( -\frac{1}{4} a^{5} + \frac{1}{4} a^{4} + a^{3} - a\) , \( -\frac{1}{2} a^{4} + \frac{1}{2} a^{3} + \frac{5}{2} a^{2} - 2 a - 2\bigr] \)
41.2-a2	\( \bigl[\frac{1}{4} a^{5} - \frac{3}{2} a^{3}\) , \( -\frac{1}{4} a^{5} + \frac{1}{4} a^{4} + \frac{5}{2} a^{3} - \frac{3}{2} a^{2} - 7 a + 1\) , \( \frac{1}{4} a^{5} - \frac{3}{2} a^{3} + \frac{1}{2} a^{2} + a - 2\) , \( \frac{1}{4} a^{5} + \frac{1}{4} a^{4} - \frac{3}{2} a^{3} - 3 a^{2} - 2 a + 6\) , \( -\frac{17}{4} a^{5} - \frac{17}{2} a^{4} + 30 a^{3} + \frac{113}{2} a^{2} - 14 a - 21\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph