Elliptic curve isogeny class 57600.1-l over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-57600.1-l
• Conductor: 57600.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 57600.1-l over \(\Q(\sqrt{-3}) \)

Isogeny class 57600.1-l contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
57600.1-l1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 110 a - 109\) , \( 731 a - 311\bigr] \)
57600.1-l2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -10 a + 11\) , \( -13 a + 1\bigr] \)
57600.1-l3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 5 a - 4\) , \( -4 a + 4\bigr] \)
57600.1-l4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 125 a - 124\) , \( 572 a - 224\bigr] \)

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