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

• Base field: \(\Q(\sqrt{6}) \)
• Label: 2.2.24.1-784.1-d
• 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-d over \(\Q(\sqrt{6}) \)

Isogeny class 784.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
784.1-d1	\( \bigl[a\) , \( 0\) , \( 0\) , \( 5 a + 13\) , \( -47 a - 115\bigr] \)
784.1-d2	\( \bigl[a\) , \( 0\) , \( 0\) , \( -295 a - 722\) , \( 3268 a + 8005\bigr] \)
784.1-d3	\( \bigl[a\) , \( 0\) , \( 0\) , \( 95 a - 232\) , \( 790 a - 1935\bigr] \)
784.1-d4	\( \bigl[a\) , \( 0\) , \( 0\) , \( -1495 a - 3662\) , \( -50000 a - 122475\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph