Elliptic curve isogeny class 50700.2-g over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-50700.2-g
• Conductor: 50700.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 50700.2-g over \(\Q(\sqrt{-3}) \)

Isogeny class 50700.2-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
50700.2-g1	\( \bigl[a\) , \( 0\) , \( 1\) , \( 288 a\) , \( 3092\bigr] \)
50700.2-g2	\( \bigl[a\) , \( 0\) , \( 1\) , \( 6208 a\) , \( 104276\bigr] \)
50700.2-g3	\( \bigl[a\) , \( 0\) , \( 1\) , \( 5408 a\) , \( 152596\bigr] \)
50700.2-g4	\( \bigl[a\) , \( 0\) , \( 1\) , \( 86528 a\) , \( 9789652\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph