Elliptic curve isogeny class 122500.2-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-122500.2-c
• Conductor: 122500.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 122500.2-c over \(\Q(\sqrt{-3}) \)

Isogeny class 122500.2-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
122500.2-c1	\( \bigl[1\) , \( -1\) , \( 0\) , \( 58\) , \( -284\bigr] \)
122500.2-c2	\( \bigl[1\) , \( -1\) , \( 0\) , \( -442\) , \( -2784\bigr] \)
122500.2-c3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -2192\) , \( 37466\bigr] \)
122500.2-c4	\( \bigl[1\) , \( -1\) , \( 0\) , \( -6692\) , \( -209034\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph