Elliptic curve isogeny class 23808.2-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-23808.2-b
• Conductor: 23808.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 23808.2-b over \(\Q(\sqrt{-3}) \)

Isogeny class 23808.2-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
23808.2-b1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -129 a + 107\) , \( -183 a + 593\bigr] \)
23808.2-b2	\( \bigl[0\) , \( 1\) , \( 0\) , \( -9 a + 7\) , \( -3 a + 9\bigr] \)
23808.2-b3	\( \bigl[0\) , \( 1\) , \( 0\) , \( 31 a - 13\) , \( a + 49\bigr] \)
23808.2-b4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -4 a + 2\) , \( a - 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph