Elliptic curve isogeny class 111.1-c over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-111.1-c
• Conductor: 111.1
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 111.1-c over \(\Q(\sqrt{3}) \)

Isogeny class 111.1-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
111.1-c1	\( \bigl[a + 1\) , \( 1\) , \( a\) , \( -5 a + 9\) , \( -19 a + 33\bigr] \)
111.1-c2	\( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 2 a + 1\) , \( 2\bigr] \)