Elliptic curve isogeny class 15876.3-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-15876.3-c
• Conductor: 15876.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 15876.3-c over \(\Q(\sqrt{-3}) \)

Isogeny class 15876.3-c contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
15876.3-c1	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -76 a + 32\) , \( -378 a + 254\bigr] \)
15876.3-c2	\( \bigl[a\) , \( a\) , \( 0\) , \( 72 a - 27\) , \( -299 a + 106\bigr] \)
15876.3-c3	\( \bigl[a\) , \( a\) , \( 0\) , \( 167 a - 277\) , \( 1305 a - 1549\bigr] \)
15876.3-c4	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -179 a + 374\) , \( 1805 a + 621\bigr] \)
15876.3-c5	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 535 a - 758\) , \( 6903 a - 6086\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph