Elliptic curve isogeny class 123627.2-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-123627.2-b
• Conductor: 123627.2
• Rank: \( 2 \)

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

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

Elliptic curves in class 123627.2-b over \(\Q(\sqrt{-3}) \)

Isogeny class 123627.2-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
123627.2-b1	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 783 a\) , \( 8720\bigr] \)
123627.2-b2	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( -12482 a\) , \( 2376092\bigr] \)
123627.2-b3	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 42468 a\) , \( -2756140\bigr] \)
123627.2-b4	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 13033 a\) , \( 528806\bigr] \)
123627.2-b5	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 12788 a\) , \( 551346\bigr] \)
123627.2-b6	\( \bigl[a\) , \( a - 1\) , \( 1\) , \( 204623 a\) , \( 35542050\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph