Elliptic curve isogeny class 15808.3-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-15808.3-a
• Conductor: 15808.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 15808.3-a over \(\Q(\sqrt{-3}) \)

Isogeny class 15808.3-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
15808.3-a1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 37 a + 59\) , \( -284 a + 306\bigr] \)
15808.3-a2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 2 a + 4\) , \( -4 a + 5\bigr] \)
15808.3-a3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 7 a - 16\) , \( -32 a + 26\bigr] \)
15808.3-a4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -8 a + 29\) , \( 52 a - 2\bigr] \)

Rank

Rank: \( 0 \)

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