Elliptic curve isogeny class 3025.1-d over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-3025.1-d
• Conductor: 3025.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 3025.1-d over \(\Q(\sqrt{3}) \)

Isogeny class 3025.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
3025.1-d1	\( \bigl[1\) , \( -1\) , \( a\) , \( -46 a + 79\) , \( 182 a - 316\bigr] \)
3025.1-d2	\( \bigl[a\) , \( 0\) , \( 0\) , \( -4\) , \( -3\bigr] \)
3025.1-d3	\( \bigl[a\) , \( 0\) , \( 0\) , \( -29\) , \( 52\bigr] \)
3025.1-d4	\( \bigl[a\) , \( 0\) , \( 0\) , \( -59\) , \( -190\bigr] \)

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