Elliptic curve isogeny class 784.1-p over number field \(\Q(\sqrt{6}) \)

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-784.1-p
• Conductor: 784.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 784.1-p over \(\Q(\sqrt{6}) \)

Isogeny class 784.1-p contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
784.1-p1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 36 a - 86\) , \( -154 a + 376\bigr] \)
784.1-p2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -132 a - 326\) , \( -1238 a - 3032\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph