Elliptic curve isogeny class 3042.1-e over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-3042.1-e
• Conductor: 3042.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 3042.1-e over \(\Q(\sqrt{3}) \)

Isogeny class 3042.1-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
3042.1-e1	\( \bigl[a\) , \( 0\) , \( 0\) , \( -3\) , \( -5\bigr] \)
3042.1-e2	\( \bigl[a\) , \( 0\) , \( 0\) , \( 270 a - 543\) , \( 3606 a - 6377\bigr] \)
3042.1-e3	\( \bigl[a\) , \( 0\) , \( 0\) , \( -63\) , \( -209\bigr] \)
3042.1-e4	\( \bigl[a\) , \( 0\) , \( 0\) , \( -270 a - 543\) , \( -3606 a - 6377\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph