Elliptic curve isogeny class 27075.2-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-27075.2-b
• Conductor: 27075.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 27075.2-b over \(\Q(\sqrt{-3}) \)

Isogeny class 27075.2-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
27075.2-b1	\( \bigl[a + 1\) , \( a\) , \( 1\) , \( 23 a - 24\) , \( -199\bigr] \)
27075.2-b2	\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -1237 a + 1236\) , \( 14291\bigr] \)
27075.2-b3	\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -382 a + 381\) , \( -2467\bigr] \)
27075.2-b4	\( \bigl[a + 1\) , \( a\) , \( 1\) , \( -6007 a + 6006\) , \( -175717\bigr] \)

Rank

Rank: \( 0 \)

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