Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-784.1-m
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-m over \(\Q(\sqrt{6}) \)

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

Curve label Weierstrass Coefficients
784.1-m1 \( \bigl[a\) , \( 0\) , \( a\) , \( -2\) , \( -1\bigr] \)
784.1-m2 \( \bigl[a\) , \( 0\) , \( a\) , \( -17\) , \( -26\bigr] \)
784.1-m3 \( \bigl[a\) , \( 0\) , \( a\) , \( -7\) , \( 0\bigr] \)
784.1-m4 \( \bigl[a\) , \( 0\) , \( a\) , \( -77\) , \( 210\bigr] \)

Rank

Rank: \( 2 \)

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