Elliptic curve isogeny class 1875.1-c over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1875.1-c
• Conductor: 1875.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1875.1-c over \(\Q(\sqrt{3}) \)

Isogeny class 1875.1-c contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
1875.1-c1	\( \bigl[a\) , \( -1\) , \( a\) , \( -2752\) , \( 104476\bigr] \)
1875.1-c2	\( \bigl[a\) , \( -1\) , \( a\) , \( -2\) , \( -24\bigr] \)
1875.1-c3	\( \bigl[a\) , \( -1\) , \( a\) , \( 873\) , \( 5226\bigr] \)
1875.1-c4	\( \bigl[a\) , \( -1\) , \( a\) , \( -252\) , \( 726\bigr] \)
1875.1-c5	\( \bigl[a\) , \( -1\) , \( a\) , \( -127\) , \( -524\bigr] \)
1875.1-c6	\( \bigl[a\) , \( -1\) , \( a\) , \( -3377\) , \( 75726\bigr] \)
1875.1-c7	\( \bigl[a\) , \( -1\) , \( a\) , \( -2002\) , \( -34274\bigr] \)
1875.1-c8	\( \bigl[a\) , \( -1\) , \( a\) , \( -54002\) , \( 4834476\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph