Elliptic curve isogeny class 1452.1-e over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1452.1-e
• Conductor: 1452.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 1452.1-e over \(\Q(\sqrt{3}) \)

Isogeny class 1452.1-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1452.1-e1	\( \bigl[0\) , \( 1\) , \( 0\) , \( 3\) , \( 0\bigr] \)
1452.1-e2	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 11 a - 23\) , \( 22 a - 40\bigr] \)
1452.1-e3	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 166 a - 293\) , \( 1661 a - 2878\bigr] \)
1452.1-e4	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 96 a - 173\) , \( -627 a + 1082\bigr] \)

Rank

Rank: \( 0 \)

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