Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-784.1-n
Conductor 784.1
Rank \( 2 \)

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-n over \(\Q(\sqrt{6}) \)

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

Curve label Weierstrass Coefficients
784.1-n1 \( \bigl[a\) , \( a + 1\) , \( a\) , \( -3\) , \( 99 a + 241\bigr] \)
784.1-n2 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 200 a - 493\) , \( -2079 a + 5091\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph