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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-50700.2-b
• Conductor: 50700.2
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
50700.2-b1	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -97 a\) , \( -297\bigr] \)
50700.2-b2	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 33 a\) , \( -63\bigr] \)
50700.2-b3	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 13 a\) , \( 13\bigr] \)
50700.2-b4	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 483 a\) , \( -4293\bigr] \)

Rank

Rank: \( 1 \)

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