Elliptic curve isogeny class 60025.3-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-60025.3-b
• Conductor: 60025.3
• Rank: \( 2 \)

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

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

Elliptic curves in class 60025.3-b over \(\Q(\sqrt{-3}) \)

Isogeny class 60025.3-b contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
60025.3-b1	\( \bigl[0\) , \( a\) , \( 1\) , \( -6435 a + 6435\) , \( 210006\bigr] \)
60025.3-b2	\( \bigl[0\) , \( a\) , \( 1\) , \( -65 a + 65\) , \( -204\bigr] \)
60025.3-b3	\( \bigl[0\) , \( a\) , \( 1\) , \( 425 a - 425\) , \( 433\bigr] \)
60025.3-b4	\( \bigl[0\) , \( a\) , \( 1\) , \( 22475 a - 24925\) , \( -1617490 a + 989498\bigr] \)
60025.3-b5	\( \bigl[0\) , \( a\) , \( 1\) , \( 24925 a - 22475\) , \( 1617490 a - 627992\bigr] \)

Rank

Rank: \( 2 \)

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