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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-392.1-d
• Conductor: 392.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
392.1-d1	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -2 a + 2\) , \( -3 a + 4\bigr] \)
392.1-d2	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 58 a - 103\) , \( 207 a - 361\bigr] \)
392.1-d3	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 18 a - 33\) , \( -73 a + 125\bigr] \)
392.1-d4	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 298 a - 523\) , \( -3993 a + 6915\bigr] \)

Rank

Rank: \( 1 \)

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