Elliptic curve isogeny class 392.1-a over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-392.1-a
• Conductor: 392.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 392.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 392.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
392.1-a1	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -a + 4\) , \( 5 a - 8\bigr] \)
392.1-a2	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 59 a - 101\) , \( -310 a + 537\bigr] \)
392.1-a3	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 19 a - 31\) , \( 40 a - 69\bigr] \)
392.1-a4	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 299 a - 521\) , \( 3470 a - 6019\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph