Elliptic curve isogeny class 10101.4-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-10101.4-a
• Conductor: 10101.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 10101.4-a over \(\Q(\sqrt{-3}) \)

Isogeny class 10101.4-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
10101.4-a1	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 8 a - 6\) , \( -11 a + 4\bigr] \)
10101.4-a2	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 13 a - 6\) , \( -8 a + 14\bigr] \)
10101.4-a3	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -62 a + 34\) , \( -21 a + 66\bigr] \)
10101.4-a4	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -497 a + 214\) , \( 3222 a - 3780\bigr] \)
10101.4-a5	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( 168 a - 46\) , \( 277 a + 542\bigr] \)
10101.4-a6	\( \bigl[a\) , \( -a\) , \( a + 1\) , \( -827 a + 494\) , \( -4816 a + 8300\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 8 & 4 & 2 & 1 & 8 & 4 \\ 4 & 2 & 4 & 8 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph