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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-363.1-b
• Conductor: 363.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
363.1-b1	\( \bigl[a\) , \( 1\) , \( a\) , \( 645 a - 1227\) , \( 12684 a - 23070\bigr] \)
363.1-b2	\( \bigl[a\) , \( 1\) , \( a\) , \( 43\) , \( -12\bigr] \)
363.1-b3	\( \bigl[a\) , \( 1\) , \( a\) , \( -12\) , \( -12\bigr] \)
363.1-b4	\( \bigl[1\) , \( -a\) , \( 1\) , \( 365 a - 632\) , \( -4716 a + 8168\bigr] \)
363.1-b5	\( \bigl[a\) , \( 1\) , \( a\) , \( -147\) , \( -768\bigr] \)
363.1-b6	\( \bigl[a\) , \( 1\) , \( a\) , \( -645 a - 1227\) , \( -12684 a - 23070\bigr] \)

Rank

Rank: \( 1 \)

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