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

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

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

Curve label	Weierstrass Coefficients
46.2-a1	\( \bigl[a^{2} + a - 1\) , \( -a^{3} - a^{2} + 3 a + 1\) , \( a^{2} - 2\) , \( -15 a^{3} + 26 a^{2} + 105 a - 60\) , \( 173 a^{3} + 83 a^{2} - 479 a + 201\bigr] \)
46.2-a2	\( \bigl[a\) , \( a + 1\) , \( a^{2} + a - 1\) , \( 0\) , \( -10 a^{3} + 18 a^{2} + 3 a - 5\bigr] \)
46.2-a3	\( \bigl[1\) , \( -a^{3} - a^{2} + 4 a + 1\) , \( a^{3} + a^{2} - 3 a - 1\) , \( -12 a^{3} + 6 a^{2} + 43 a - 23\) , \( -32 a^{3} - a^{2} + 136 a - 33\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph