Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-784.1-c
Conductor 784.1
Rank \( 0 \)

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Base field \(\Q(\sqrt{-2}) \)

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

Elliptic curves in class 784.1-c over \(\Q(\sqrt{-2}) \)

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

Curve label Weierstrass Coefficients
784.1-c1 \( \bigl[a\) , \( 1\) , \( 0\) , \( -682\) , \( -6990\bigr] \)
784.1-c2 \( \bigl[a\) , \( 1\) , \( 0\) , \( -2\) , \( 2\bigr] \)
784.1-c3 \( \bigl[a\) , \( 1\) , \( 0\) , \( 18\) , \( -46\bigr] \)
784.1-c4 \( \bigl[a\) , \( 1\) , \( 0\) , \( -142\) , \( -558\bigr] \)
784.1-c5 \( \bigl[a\) , \( 1\) , \( 0\) , \( -42\) , \( 98\bigr] \)
784.1-c6 \( \bigl[a\) , \( 1\) , \( 0\) , \( -10922\) , \( -441166\bigr] \)

Rank

Rank: \( 0 \)

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