Elliptic curve isogeny class 99372.5-k over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-99372.5-k
• Conductor: 99372.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 99372.5-k over \(\Q(\sqrt{-3}) \)

Isogeny class 99372.5-k contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
99372.5-k1	\( \bigl[a\) , \( 0\) , \( 1\) , \( 26056 a\) , \( -1621108\bigr] \)
99372.5-k2	\( \bigl[a\) , \( 0\) , \( 1\) , \( 3361 a - 21480\) , \( 271392 a - 1198804\bigr] \)
99372.5-k3	\( \bigl[a\) , \( 0\) , \( 1\) , \( 121 a\) , \( -4948\bigr] \)
99372.5-k4	\( \bigl[a\) , \( 0\) , \( 1\) , \( -14 a\) , \( 182\bigr] \)
99372.5-k5	\( \bigl[a\) , \( 0\) , \( 1\) , \( -18119 a + 21480\) , \( -271392 a - 927412\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrr} 1 & 9 & 3 & 9 & 9 \\ 9 & 1 & 3 & 9 & 9 \\ 3 & 3 & 1 & 3 & 3 \\ 9 & 9 & 3 & 1 & 9 \\ 9 & 9 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph