Elliptic curve isogeny class 46.2-d over number field \(\Q(\sqrt{2}, \sqrt{3})\)

• Base field: \(\Q(\sqrt{2}, \sqrt{3})\)
• Label: 4.4.2304.1-46.2-d
• Conductor: 46.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{2}, \sqrt{3})\)

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

Elliptic curves in class 46.2-d over \(\Q(\sqrt{2}, \sqrt{3})\)

Isogeny class 46.2-d contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
46.2-d1	\( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( a^{3} - 4 a + 1\) , \( a^{3} + a^{2} - 4 a - 2\) , \( -12 a^{3} + 27 a^{2} + 94 a - 61\) , \( -186 a^{3} - 56 a^{2} + 577 a - 263\bigr] \)
46.2-d2	\( \bigl[a^{3} - 4 a\) , \( -a + 1\) , \( a^{2} - 1\) , \( a^{3} - 4 a + 1\) , \( 10 a^{3} - 19 a^{2} - 4 a + 5\bigr] \)
46.2-d3	\( \bigl[a^{2} - 2\) , \( a^{3} + a^{2} - 4 a - 2\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -11 a^{3} + 6 a^{2} + 39 a - 24\) , \( 32 a^{3} - 138 a + 32\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph