Elliptic curve isogeny class 126976.2-f over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-126976.2-f
• Conductor: 126976.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 126976.2-f over \(\Q(\sqrt{-3}) \)

Isogeny class 126976.2-f contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
126976.2-f1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 35167 a - 83199\) , \( 5257632 a - 8569025\bigr] \)
126976.2-f2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -33 a + 1\) , \( 32 a - 65\bigr] \)
126976.2-f3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -353 a + 961\) , \( 416 a + 5503\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph