Elliptic curve isogeny class 63948.2-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-63948.2-c
• Conductor: 63948.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 63948.2-c over \(\Q(\sqrt{-3}) \)

Isogeny class 63948.2-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
63948.2-c1	\( \bigl[a\) , \( 0\) , \( 1\) , \( 32680 a\) , \( 1883180\bigr] \)
63948.2-c2	\( \bigl[a\) , \( 0\) , \( 1\) , \( 9640 a\) , \( -337876\bigr] \)
63948.2-c3	\( \bigl[a\) , \( 0\) , \( 1\) , \( 1945 a\) , \( 32780\bigr] \)
63948.2-c4	\( \bigl[a\) , \( 0\) , \( 1\) , \( 31105 a\) , \( 2108972\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph