Elliptic curve isogeny class 3468.1-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-3468.1-c
• Conductor: 3468.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 3468.1-c over \(\Q(\sqrt{-3}) \)

Isogeny class 3468.1-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
3468.1-c1	\( \bigl[a\) , \( 0\) , \( 1\) , \( 215 a\) , \( 2062\bigr] \)
3468.1-c2	\( \bigl[a\) , \( 0\) , \( 1\) , \( -1810 a\) , \( -37790\bigr] \)
3468.1-c3	\( \bigl[a\) , \( 0\) , \( 1\) , \( 750 a\) , \( -6046\bigr] \)
3468.1-c4	\( \bigl[a\) , \( 0\) , \( 1\) , \( 255 a\) , \( 1550\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph