Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-784.1-k
Conductor 784.1
Rank not recorded

Related objects

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

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

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

Isogeny class 784.1-k contains 6 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
784.1-k1 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -13642 a - 33423\) , \( 1370379 a + 3356729\bigr] \)
784.1-k2 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -42 a - 103\) , \( -437 a - 1071\bigr] \)
784.1-k3 \( \bigl[a\) , \( a - 1\) , \( a\) , \( -358 a + 877\) , \( -9467 a + 23189\bigr] \)
784.1-k4 \( \bigl[a\) , \( a - 1\) , \( a\) , \( 2842 a - 6963\) , \( -107643 a + 263669\bigr] \)
784.1-k5 \( \bigl[a\) , \( a - 1\) , \( a\) , \( 842 a - 2063\) , \( 20245 a - 49591\bigr] \)
784.1-k6 \( \bigl[a\) , \( a - 1\) , \( a\) , \( 218442 a - 535183\) , \( -87132427 a + 213430329\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph