Elliptic curve isogeny class 2028.1-g over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-2028.1-g
• Conductor: 2028.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 2028.1-g over \(\Q(\sqrt{3}) \)

Isogeny class 2028.1-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
2028.1-g1	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 315 a - 546\) , \( 4127 a - 7149\bigr] \)
2028.1-g2	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 20 a - 36\) , \( 65 a - 114\bigr] \)
2028.1-g3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -5\) , \( 6\bigr] \)
2028.1-g4	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -35 a + 54\) , \( 293 a - 519\bigr] \)

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