Elliptic curve isogeny class 65856.3-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-65856.3-c
• Conductor: 65856.3
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 65856.3-c over \(\Q(\sqrt{-3}) \)

Isogeny class 65856.3-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
65856.3-c1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -1151 a + 826\) , \( 6309 a - 14838\bigr] \)
65856.3-c2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -3611 a + 8486\) , \( 234601 a + 27418\bigr] \)
65856.3-c3	\( \bigl[0\) , \( -1\) , \( 0\) , \( 2389 a - 5034\) , \( 43769 a - 127302\bigr] \)
65856.3-c4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -1091 a + 926\) , \( 10321 a - 15926\bigr] \)