Elliptic curve isogeny class 27075.3-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-27075.3-a
• Conductor: 27075.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 27075.3-a over \(\Q(\sqrt{-3}) \)

Isogeny class 27075.3-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
27075.3-a1	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 18 a - 13\) , \( -100 a + 99\bigr] \)
27075.3-a2	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 383 a - 463\) , \( -3669 a + 2526\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph