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

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-576.1-e
• Conductor: 576.1
• Rank: \( 1 \)

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

Generator \(a\), with minimal polynomial \( x^{2} - 7 \); class number \(1\).

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

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

Curve label	Weierstrass Coefficients
576.1-e1	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 391 a + 1034\) , \( 5664 a + 14985\bigr] \)
576.1-e2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -8\) , \( 6 a\bigr] \)
576.1-e3	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -391 a + 1034\) , \( 4882 a - 12917\bigr] \)
576.1-e4	\( \bigl[0\) , \( -a\) , \( 0\) , \( -1744 a - 4612\) , \( 66006 a + 174636\bigr] \)

Rank

Rank: \( 1 \)

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