Elliptic curve isogeny class 22.2-b over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-22.2-b
• Conductor: 22.2
• Rank: \( 0 \)

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

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 22.2-b over \(\Q(\sqrt{3}) \)

Isogeny class 22.2-b contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
22.2-b1	\( \bigl[a\) , \( -1\) , \( a\) , \( 1813 a - 3143\) , \( 55168 a - 95555\bigr] \)
22.2-b2	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -20 a - 32\) , \( 64 a + 112\bigr] \)
22.2-b3	\( \bigl[a\) , \( -1\) , \( a\) , \( 1688 a - 2923\) , \( 63194 a - 109459\bigr] \)
22.2-b4	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 3\) , \( 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph