Elliptic curve isogeny class 363.1-a over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-363.1-a
• Conductor: 363.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 363.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 363.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
363.1-a1	\( \bigl[1\) , \( 1\) , \( 0\) , \( 645 a - 1226\) , \( -12039 a + 21843\bigr] \)
363.1-a2	\( \bigl[1\) , \( 1\) , \( 0\) , \( 44\) , \( 55\bigr] \)
363.1-a3	\( \bigl[1\) , \( 1\) , \( 0\) , \( -11\) , \( 0\bigr] \)
363.1-a4	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 365 a - 633\) , \( 4716 a - 8169\bigr] \)
363.1-a5	\( \bigl[1\) , \( 1\) , \( 0\) , \( -146\) , \( 621\bigr] \)
363.1-a6	\( \bigl[1\) , \( 1\) , \( 0\) , \( -645 a - 1226\) , \( 12039 a + 21843\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph