Elliptic curve isogeny class 1225.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-1225.2-a
• Conductor: 1225.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 1225.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 1225.2-a contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
1225.2-a1	\( \bigl[0\) , \( 1\) , \( 1\) , \( -131\) , \( -650\bigr] \)
1225.2-a2	\( \bigl[0\) , \( -a\) , \( 1\) , \( -a + 1\) , \( 0\bigr] \)
1225.2-a3	\( \bigl[0\) , \( -a\) , \( 1\) , \( 9 a - 9\) , \( 1\bigr] \)
1225.2-a4	\( \bigl[0\) , \( -a\) , \( 1\) , \( 509 a - 459\) , \( -4730 a + 1976\bigr] \)
1225.2-a5	\( \bigl[0\) , \( -a\) , \( 1\) , \( 459 a - 509\) , \( 4730 a - 2754\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph