Elliptic curve isogeny class 15876.1-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-15876.1-c
• Conductor: 15876.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 15876.1-c over \(\Q(\sqrt{-3}) \)

Isogeny class 15876.1-c contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
15876.1-c1	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( 194 a - 373\) , \( -1806 a + 2426\bigr] \)
15876.1-c2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -44 a - 31\) , \( 377 a - 123\bigr] \)
15876.1-c3	\( \bigl[a\) , \( -1\) , \( 0\) , \( 45 a + 27\) , \( 299 a - 193\bigr] \)
15876.1-c4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -110 a + 277\) , \( -1305 a - 244\bigr] \)
15876.1-c5	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 760 a - 536\) , \( -6679 a + 58\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrr} 1 & 3 & 9 & 9 & 9 \\ 3 & 1 & 3 & 3 & 3 \\ 9 & 3 & 1 & 9 & 9 \\ 9 & 3 & 9 & 1 & 9 \\ 9 & 3 & 9 & 9 & 1 \end{array}\right)\)

Isogeny graph