Elliptic curve isogeny class 134199.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-134199.2-a
• Conductor: 134199.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 134199.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 134199.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
134199.2-a1	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 54 a - 28\) , \( -92 a - 28\bigr] \)
134199.2-a2	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 384 a + 242\) , \( -3266 a + 5966\bigr] \)
134199.2-a3	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 54 a - 13\) , \( -167 a + 71\bigr] \)
134199.2-a4	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -276 a - 28\) , \( -1628 a + 212\bigr] \)

Rank

Rank: \( 1 \)

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