Elliptic curve isogeny class 194.1-c over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-194.1-c
• Number of curves: 4
• Conductor: 194.1
• Rank: \( 0 \)

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

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

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

Elliptic curves in class 194.1-c over \(\Q(\sqrt{3}) \)

Isogeny class 194.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
194.1-c1	\( \bigl[a\) , \( -a\) , \( a\) , \( 185 a - 317\) , \( 1939 a - 3372\bigr] \)
194.1-c2	\( \bigl[a\) , \( -a\) , \( a\) , \( -2\) , \( a - 2\bigr] \)
194.1-c3	\( \bigl[a\) , \( -a\) , \( a\) , \( 10 a - 22\) , \( 37 a - 66\bigr] \)
194.1-c4	\( \bigl[a\) , \( -a\) , \( a\) , \( -5 a - 47\) , \( -a - 136\bigr] \)