Elliptic curve isogeny class 4802.1-a over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-4802.1-a
• Conductor: 4802.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 4802.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 4802.1-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
4802.1-a1	\( \bigl[1\) , \( 1\) , \( 0\) , \( -8355\) , \( 291341\bigr] \)
4802.1-a2	\( \bigl[1\) , \( 1\) , \( 0\) , \( -25\) , \( -111\bigr] \)
4802.1-a3	\( \bigl[1\) , \( 1\) , \( 0\) , \( 220\) , \( 2192\bigr] \)
4802.1-a4	\( \bigl[1\) , \( 1\) , \( 0\) , \( -1740\) , \( 22184\bigr] \)
4802.1-a5	\( \bigl[1\) , \( 1\) , \( 0\) , \( -515\) , \( -4717\bigr] \)
4802.1-a6	\( \bigl[1\) , \( 1\) , \( 0\) , \( -133795\) , \( 18781197\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph