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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-15876.1-b
• 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-b over \(\Q(\sqrt{-3}) \)

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

Curve label	Weierstrass Coefficients
15876.1-b1	\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -180 a - 12\) , \( 970 a - 392\bigr] \)
15876.1-b2	\( \bigl[a\) , \( -1\) , \( 1\) , \( -142 a + 214\) , \( -493 a - 666\bigr] \)
15876.1-b3	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 28 a - 76\) , \( 152 a - 258\bigr] \)
15876.1-b4	\( \bigl[a\) , \( -1\) , \( 1\) , \( 13 a - 36\) , \( -65 a + 120\bigr] \)
15876.1-b5	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -13 a + 32\) , \( -33 a + 50\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph