Elliptic curve isogeny class 2178.1-d over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-2178.1-d
• Conductor: 2178.1
• Rank: \( 0 \)

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

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 2178.1-d over \(\Q(\sqrt{3}) \)

Isogeny class 2178.1-d contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
2178.1-d1	\( \bigl[1\) , \( -1\) , \( 1\) , \( 4440 a - 8705\) , \( -230640 a + 412625\bigr] \)
2178.1-d2	\( \bigl[a\) , \( 0\) , \( 0\) , \( 690 a - 627\) , \( -8070 a + 15471\bigr] \)
2178.1-d3	\( \bigl[a\) , \( 0\) , \( 0\) , \( -147\) , \( 135\bigr] \)
2178.1-d4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -65\) , \( 209\bigr] \)
2178.1-d5	\( \bigl[a\) , \( 0\) , \( 0\) , \( -87\) , \( -333\bigr] \)
2178.1-d6	\( \bigl[a\) , \( 0\) , \( 0\) , \( -690 a - 627\) , \( 8070 a + 15471\bigr] \)
2178.1-d7	\( \bigl[1\) , \( -1\) , \( 1\) , \( -1025\) , \( 12881\bigr] \)
2178.1-d8	\( \bigl[1\) , \( -1\) , \( 1\) , \( -4440 a - 8705\) , \( 230640 a + 412625\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 6 & 4 & 12 & 12 & 2 & 4 \\ 3 & 1 & 2 & 12 & 4 & 4 & 6 & 12 \\ 6 & 2 & 1 & 6 & 2 & 2 & 3 & 6 \\ 4 & 12 & 6 & 1 & 3 & 12 & 2 & 4 \\ 12 & 4 & 2 & 3 & 1 & 4 & 6 & 12 \\ 12 & 4 & 2 & 12 & 4 & 1 & 6 & 3 \\ 2 & 6 & 3 & 2 & 6 & 6 & 1 & 2 \\ 4 & 12 & 6 & 4 & 12 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph