Elliptic curve isogeny class 1250.1-d over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1250.1-d
• Conductor: 1250.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1250.1-d over \(\Q(\sqrt{3}) \)

Isogeny class 1250.1-d contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
1250.1-d1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -3138\) , \( -68969\bigr] \)
1250.1-d2	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 169 a - 292\) , \( -2012 a + 3485\bigr] \)
1250.1-d3	\( \bigl[1\) , \( 1\) , \( 1\) , \( -13\) , \( -219\bigr] \)
1250.1-d4	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -1231 a + 2133\) , \( 14838 a - 25700\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph