Elliptic Curve Isogeny Class 54948.1-e over Number Field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-54948.1-e
• Conductor: 54948.1
• Rank: not recorded

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

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

Elliptic curves in class 54948.1-e over \(\Q(\sqrt{-3}) \)

Isogeny class 54948.1-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
54948.1-e1	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -16394 a + 21429\) , \( -402620 a - 768660\bigr] \)
54948.1-e2	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -64 a + 79\) , \( -144 a - 136\bigr] \)
54948.1-e3	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -384 a + 99\) , \( -3184 a + 2464\bigr] \)
54948.1-e4	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( 16 a - 1\) , \( 16 a - 40\bigr] \)
54948.1-e5	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -1014 a + 1409\) , \( -3988 a - 11996\bigr] \)
54948.1-e6	\( \bigl[a\) , \( a + 1\) , \( 1\) , \( -1024 a + 1339\) , \( -6384 a - 11440\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph