Elliptic curve isogeny class 4800.1-l over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-4800.1-l
• Conductor: 4800.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 4800.1-l over \(\Q(\sqrt{3}) \)

Isogeny class 4800.1-l contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
4800.1-l1	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -24 a + 41\) , \( 21 a - 37\bigr] \)
4800.1-l2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -6\) , \( 0\bigr] \)
4800.1-l3	\( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 57 a - 97\) , \( -281 a + 487\bigr] \)
4800.1-l4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( -82 a - 141\) , \( -549 a - 951\bigr] \)

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