Elliptic curve isogeny class 102400.1-k over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-102400.1-k
• Conductor: 102400.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 102400.1-k over \(\Q(\sqrt{-3}) \)

Isogeny class 102400.1-k contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
102400.1-k1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 165 a - 164\) , \( 1118 a - 641\bigr] \)
102400.1-k2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 124\) , \( 126 a - 125\bigr] \)
102400.1-k3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 516\) , \( 1534 a - 509\bigr] \)
102400.1-k4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 2725 a - 2724\) , \( 64094 a - 33409\bigr] \)

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