Elliptic curve isogeny class 22.1-a over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-22.1-a
• Conductor: 22.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 22.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 22.1-a contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
22.1-a1	\( \bigl[1\) , \( a\) , \( a + 1\) , \( 14261 a - 24701\) , \( -1229141 a + 2128933\bigr] \)
22.1-a2	\( \bigl[1\) , \( a\) , \( a + 1\) , \( -23694 a + 41039\) , \( -5992615 a + 10379512\bigr] \)
22.1-a3	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 18 a - 33\) , \( 83 a - 145\bigr] \)
22.1-a4	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -2 a + 2\) , \( -a + 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph