Elliptic curve isogeny class 87808.2-k over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-87808.2-k
• Conductor: 87808.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 87808.2-k over \(\Q(\sqrt{-3}) \)

Isogeny class 87808.2-k contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
87808.2-k1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -388 a + 384\) , \( -92 a - 2696\bigr] \)
87808.2-k2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 132 a + 304\) , \( 3252 a - 2728\bigr] \)
87808.2-k3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -8 a + 24\) , \( 60 a - 96\bigr] \)
87808.2-k4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 7 a - 16\) , \( 10 a - 28\bigr] \)

Rank

Rank: \( 1 \)

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