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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-392.1-c
• 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-c over \(\Q(\sqrt{3}) \)

Isogeny class 392.1-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
392.1-c1	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -a - 2\) , \( 7 a + 12\bigr] \)
392.1-c2	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -41 a - 72\) , \( 157 a + 272\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph