Elliptic curve isogeny class 99372.4-g over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-99372.4-g
• Conductor: 99372.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 99372.4-g over \(\Q(\sqrt{-3}) \)

Isogeny class 99372.4-g contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
99372.4-g1	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -31 a + 60\) , \( 243 a + 152\bigr] \)
99372.4-g2	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 3089 a - 5790\) , \( 40575 a + 15536\bigr] \)
99372.4-g3	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -831 a + 1560\) , \( 5099 a + 3384\bigr] \)
99372.4-g4	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -7311 a + 13710\) , \( -380137 a - 170928\bigr] \)
99372.4-g5	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -671 a + 1260\) , \( 10579 a + 5784\bigr] \)
99372.4-g6	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( -10751 a + 20160\) , \( 681403 a + 334392\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph