Elliptic curve isogeny class 3072.1-w over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-3072.1-w
• Conductor: 3072.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 3072.1-w over \(\Q(\sqrt{3}) \)

Isogeny class 3072.1-w contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
3072.1-w1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 468 a - 808\) , \( 7028 a - 12172\bigr] \)
3072.1-w2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 58 a - 98\) , \( -152 a + 264\bigr] \)
3072.1-w3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 768 a - 1328\) , \( -15408 a + 26688\bigr] \)
3072.1-w4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -4 a + 6\) , \( -4 a + 6\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph