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

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-784.1-i
• Conductor: 784.1
• Rank: \( 1 \)

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

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

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

Isogeny class 784.1-i contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
784.1-i1	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( a - 2\) , \( 2 a - 5\bigr] \)
784.1-i2	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 61 a - 142\) , \( -338 a + 827\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph