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

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-578.1-e
• Conductor: 578.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
578.1-e1	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 39 a - 250\) , \( -213 a + 1222\bigr] \)
578.1-e2	\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( 19 a - 50\) , \( 99 a - 242\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph