Elliptic curve isogeny class 2304.1-v over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-2304.1-v
• Conductor: 2304.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 2304.1-v over \(\Q(\sqrt{3}) \)

Isogeny class 2304.1-v contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
2304.1-v1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -15 a - 26\bigr] \)
2304.1-v2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 15 a + 26\bigr] \)
2304.1-v3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -120 a - 225\) , \( -510 a - 856\bigr] \)
2304.1-v4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -120 a - 225\) , \( 510 a + 856\bigr] \)
2304.1-v5	\( \bigl[0\) , \( 0\) , \( 0\) , \( -60 a - 105\) , \( -330 a - 572\bigr] \)
2304.1-v6	\( \bigl[0\) , \( 0\) , \( 0\) , \( -60 a - 105\) , \( 330 a + 572\bigr] \)
2304.1-v7	\( \bigl[0\) , \( 0\) , \( 0\) , \( -960 a - 1665\) , \( -21330 a - 36944\bigr] \)
2304.1-v8	\( \bigl[0\) , \( 0\) , \( 0\) , \( -960 a - 1665\) , \( 21330 a + 36944\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph