Elliptic curve isogeny class 87808.3-j over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-87808.3-j
• Conductor: 87808.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 87808.3-j over \(\Q(\sqrt{-3}) \)

Isogeny class 87808.3-j contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
87808.3-j1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -5 a + 8\) , \( -36 a + 38\bigr] \)
87808.3-j2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 295 a - 472\) , \( 2484 a - 2622\bigr] \)
87808.3-j3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 95 a - 152\) , \( -540 a + 570\bigr] \)
87808.3-j4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 1495 a - 2392\) , \( -35820 a + 37810\bigr] \)

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