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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-50700.2-c
• 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-c over \(\Q(\sqrt{-3}) \)

Isogeny class 50700.2-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
50700.2-c1	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -114 a + 114\) , \( -12978\bigr] \)
50700.2-c2	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 16 a - 16\) , \( 0\bigr] \)
50700.2-c3	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -64 a + 64\) , \( 112\bigr] \)
50700.2-c4	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -564 a + 564\) , \( -4788\bigr] \)
50700.2-c5	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -844 a + 844\) , \( 9940\bigr] \)
50700.2-c6	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -9014 a + 9014\) , \( -324198\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph