Elliptic curve isogeny class 43776.1-h over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-43776.1-h
• Conductor: 43776.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 43776.1-h over \(\Q(\sqrt{-3}) \)

Isogeny class 43776.1-h contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
43776.1-h1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -46 a - 337\) , \( 659 a + 2461\bigr] \)
43776.1-h2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -a - 22\) , \( 20 a + 40\bigr] \)
43776.1-h3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -31 a + 53\) , \( -13 a + 208\bigr] \)
43776.1-h4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 44 a - 112\) , \( 272 a - 356\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph