Elliptic curve isogeny class 676.2-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-676.2-b
• Conductor: 676.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 676.2-b over \(\Q(\sqrt{-3}) \)

Isogeny class 676.2-b contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
676.2-b1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -460\) , \( -3830\bigr] \)
676.2-b2	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -5 a + 4\) , \( -8\bigr] \)
676.2-b3	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -1\) , \( 0\bigr] \)
676.2-b4	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 135 a + 94\) , \( 724 a - 1240\bigr] \)
676.2-b5	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -95 a - 136\) , \( -724 a - 516\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrr} 1 & 3 & 9 & 9 & 9 \\ 3 & 1 & 3 & 3 & 3 \\ 9 & 3 & 1 & 9 & 9 \\ 9 & 3 & 9 & 1 & 9 \\ 9 & 3 & 9 & 9 & 1 \end{array}\right)\)

Isogeny graph