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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-43776.1-m
• 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-m over \(\Q(\sqrt{-3}) \)

Isogeny class 43776.1-m contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
43776.1-m1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2630 a + 1711\) , \( 15625 a - 48369\bigr] \)
43776.1-m2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 10 a + 31\) , \( 25 a + 255\bigr] \)
43776.1-m3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 5050 a + 1711\) , \( 232201 a - 312561\bigr] \)
43776.1-m4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 10 a - 449\) , \( -359 a + 3231\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)

Isogeny graph