Elliptic Curve Isogeny Class 54948.4-e over Number Field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-54948.4-e
• Conductor: 54948.4
• Rank: not recorded

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

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

Elliptic curves in class 54948.4-e over \(\Q(\sqrt{-3}) \)

Isogeny class 54948.4-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
54948.4-e1	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 5035 a - 21429\) , \( 402620 a - 1171280\bigr] \)
54948.4-e2	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 315 a - 1339\) , \( 6384 a - 17824\bigr] \)
54948.4-e3	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -285 a - 99\) , \( 3184 a - 720\bigr] \)
54948.4-e4	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 15 a + 1\) , \( -16 a - 24\bigr] \)
54948.4-e5	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 15 a - 79\) , \( 144 a - 280\bigr] \)
54948.4-e6	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( 395 a - 1409\) , \( 3988 a - 15984\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 8 & 4 & 4 \\ 2 & 1 & 4 & 4 & 2 & 2 \\ 8 & 4 & 1 & 4 & 2 & 8 \\ 8 & 4 & 4 & 1 & 2 & 8 \\ 4 & 2 & 2 & 2 & 1 & 4 \\ 4 & 2 & 8 & 8 & 4 & 1 \end{array}\right)\)

Isogeny graph