Elliptic curve isogeny class 578.1-b over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-578.1-b
• Conductor: 578.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{6}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 6 \); class number \(1\).

Elliptic curves in class 578.1-b over \(\Q(\sqrt{6}) \)

Isogeny class 578.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
578.1-b1	\( \bigl[1\) , \( -a\) , \( a\) , \( -3057 a - 7488\) , \( -141756 a - 347236\bigr] \)
578.1-b2	\( \bigl[1\) , \( -a\) , \( a\) , \( -37 a - 88\) , \( -184 a - 452\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph