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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-87808.3-i
• 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-i over \(\Q(\sqrt{-3}) \)

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

Curve label	Weierstrass Coefficients
87808.3-i1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -130 a + 435\) , \( -3121 a + 89\bigr] \)
87808.3-i2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 390 a - 5\) , \( -297 a - 2783\bigr] \)
87808.3-i3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 10 a + 15\) , \( -69 a - 51\bigr] \)
87808.3-i4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -5 a - 10\) , \( -4 a - 8\bigr] \)

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