Elliptic curve isogeny class 4900.3-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-4900.3-a
• Conductor: 4900.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 4900.3-a over \(\Q(\sqrt{-3}) \)

Isogeny class 4900.3-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
4900.3-a1	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 20 a - 8\) , \( 25 a + 21\bigr] \)
4900.3-a2	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( 6 a + 10\) , \( 0\bigr] \)
4900.3-a3	\( \bigl[a + 1\) , \( -a - 1\) , \( 0\) , \( -24 a - 40\) , \( 40 a + 34\bigr] \)
4900.3-a4	\( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 340 a - 128\) , \( 1305 a + 1109\bigr] \)

Rank

Rank: \( 1 \)

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