Elliptic curve isogeny class 23808.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-23808.1-a
• Conductor: 23808.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 23808.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 23808.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
23808.1-a1	\( \bigl[0\) , \( a\) , \( 0\) , \( -2 a - 2\) , \( a + 1\bigr] \)
23808.1-a2	\( \bigl[0\) , \( a\) , \( 0\) , \( 18 a + 13\) , \( a - 50\bigr] \)
23808.1-a3	\( \bigl[0\) , \( a\) , \( 0\) , \( -2 a - 7\) , \( -3 a - 6\bigr] \)
23808.1-a4	\( \bigl[0\) , \( a\) , \( 0\) , \( -22 a - 107\) , \( -183 a - 410\bigr] \)

Rank

Rank: \( 0 \)

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