Elliptic curve isogeny class 578.1-b over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-578.1-b
• Conductor: 578.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 578.1-b over \(\Q(\sqrt{7}) \)

Isogeny class 578.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
578.1-b1	\( \bigl[a\) , \( 1\) , \( a\) , \( -4\) , \( -5\bigr] \)
578.1-b2	\( \bigl[a\) , \( 1\) , \( a\) , \( -114\) , \( 215\bigr] \)
578.1-b3	\( \bigl[a\) , \( 1\) , \( a\) , \( -44\) , \( -149\bigr] \)
578.1-b4	\( \bigl[a\) , \( 1\) , \( a\) , \( -104\) , \( 307\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph