Elliptic curve isogeny class 6348.1-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-6348.1-c
• Conductor: 6348.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 6348.1-c over \(\Q(\sqrt{-3}) \)

Isogeny class 6348.1-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
6348.1-c1	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -36 a + 35\) , \( 82\bigr] \)
6348.1-c2	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 189 a - 190\) , \( 190\bigr] \)
6348.1-c3	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -771 a + 770\) , \( 1342\bigr] \)
6348.1-c4	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( -576 a + 575\) , \( 5266\bigr] \)

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