Elliptic curve isogeny class 30625.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-30625.2-a
• Conductor: 30625.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 30625.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 30625.2-a contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
30625.2-a1	\( \bigl[0\) , \( a\) , \( 1\) , \( -3283 a + 3283\) , \( -74657\bigr] \)
30625.2-a2	\( \bigl[0\) , \( a\) , \( 1\) , \( -33 a + 33\) , \( 93\bigr] \)
30625.2-a3	\( \bigl[0\) , \( a\) , \( 1\) , \( 217 a - 217\) , \( -282\bigr] \)
30625.2-a4	\( \bigl[0\) , \( a\) , \( 1\) , \( 11467 a - 12717\) , \( 588750 a - 367157\bigr] \)
30625.2-a5	\( \bigl[0\) , \( a\) , \( 1\) , \( 12717 a - 11467\) , \( -588750 a + 221593\bigr] \)

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