Elliptic curve isogeny class 7203.3-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-7203.3-a
• Conductor: 7203.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 7203.3-a over \(\Q(\sqrt{-3}) \)

Isogeny class 7203.3-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
7203.3-a1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -23030 a + 15728\) , \( -663068 a + 1309524\bigr] \)
7203.3-a2	\( \bigl[1\) , \( 1\) , \( 1\) , \( 23030 a - 7302\) , \( 663068 a + 646456\bigr] \)
7203.3-a3	\( \bigl[1\) , \( 1\) , \( 1\) , \( -1667\) , \( 72764\bigr] \)
7203.3-a4	\( \bigl[1\) , \( 1\) , \( 1\) , \( 48\) , \( 48\bigr] \)
7203.3-a5	\( \bigl[1\) , \( 1\) , \( 1\) , \( -197\) , \( 146\bigr] \)
7203.3-a6	\( \bigl[1\) , \( 1\) , \( 1\) , \( -1912\) , \( -32782\bigr] \)
7203.3-a7	\( \bigl[1\) , \( 1\) , \( 1\) , \( -2402\) , \( 44246\bigr] \)
7203.3-a8	\( \bigl[1\) , \( 1\) , \( 1\) , \( -38417\) , \( 2882228\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 16 & 8 & 16 & 4 & 8 \\ 4 & 1 & 2 & 16 & 8 & 16 & 4 & 8 \\ 2 & 2 & 1 & 8 & 4 & 8 & 2 & 4 \\ 16 & 16 & 8 & 1 & 2 & 4 & 4 & 8 \\ 8 & 8 & 4 & 2 & 1 & 2 & 2 & 4 \\ 16 & 16 & 8 & 4 & 2 & 1 & 4 & 8 \\ 4 & 4 & 2 & 4 & 2 & 4 & 1 & 2 \\ 8 & 8 & 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph