Elliptic curve isogeny class 75625.1-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-75625.1-b
• Conductor: 75625.1
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 75625.1-b over \(\Q(\sqrt{-3}) \)

Isogeny class 75625.1-b contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
75625.1-b1	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 195508 a\) , \( -33338481\bigr] \)
75625.1-b2	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 258 a\) , \( -2981\bigr] \)
75625.1-b3	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( 8 a\) , \( 19\bigr] \)