Elliptic curve isogeny class 576.1-a over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-576.1-a
• Conductor: 576.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-7}) \)

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

Elliptic curves in class 576.1-a over \(\Q(\sqrt{-7}) \)

Isogeny class 576.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
576.1-a1	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -3 a\) , \( -2 a + 3\bigr] \)
576.1-a2	\( \bigl[a\) , \( a\) , \( 0\) , \( a + 1\) , \( 2 a - 3\bigr] \)
576.1-a3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -a - 1\) , \( a + 2\bigr] \)
576.1-a4	\( \bigl[a\) , \( a\) , \( 0\) , \( 16 a + 31\) , \( 83 a - 129\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph