Elliptic curve isogeny class 69312.3-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-69312.3-a
• Conductor: 69312.3
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 69312.3-a over \(\Q(\sqrt{-3}) \)

Isogeny class 69312.3-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
69312.3-a1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -24 a + 53\) , \( -100 a - 48\bigr] \)
69312.3-a2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 416 a - 712\) , \( -5408 a + 7228\bigr] \)
69312.3-a3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -104 a + 28\) , \( -624 a + 420\bigr] \)
69312.3-a4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -1904 a + 368\) , \( -30656 a + 23164\bigr] \)