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

• Base field: \(\Q(\sqrt{2}, \sqrt{3})\)
• Label: 4.4.2304.1-46.2-b
• 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-b over \(\Q(\sqrt{2}, \sqrt{3})\)

Isogeny class 46.2-b contains 2 curves linked by isogenies of degree 11.

Curve label	Weierstrass Coefficients
46.2-b1	\( \bigl[a^{3} - 4 a\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a + 1\) , \( a^{3} - 3 a + 2\) , \( 13 a^{3} - 7 a^{2} - 49 a + 25\bigr] \)
46.2-b2	\( \bigl[a^{3} + a^{2} - 4 a - 1\) , \( a^{3} - 3 a - 1\) , \( a^{2} - 2\) , \( 664 a^{3} + 475 a^{2} - 2535 a - 1969\) , \( 17976 a^{3} + 10669 a^{2} - 67414 a - 41406\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph