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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-3072.1-ca
• Conductor: 3072.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
3072.1-ca1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 504 a - 872\) , \( 2120 a - 3672\bigr] \)
3072.1-ca2	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 284 a - 492\) , \( -3672 a + 6360\bigr] \)
3072.1-ca3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 4544 a - 7872\) , \( -223656 a + 387384\bigr] \)
3072.1-ca4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 4 a - 7\) , \( -134 a + 232\bigr] \)

Rank

Rank: \( 1 \)

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