Elliptic curve isogeny class 2500.1-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-2500.1-b
• Conductor: 2500.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 2500.1-b over \(\Q(\sqrt{-3}) \)

Isogeny class 2500.1-b contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
2500.1-b1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( -552\bigr] \)
2500.1-b2	\( \bigl[1\) , \( 0\) , \( 1\) , \( -76\) , \( 298\bigr] \)
2500.1-b3	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -a\) , \( -2\bigr] \)
2500.1-b4	\( \bigl[1\) , \( 0\) , \( 1\) , \( 549\) , \( -2202\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph