Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-784.1-c
Conductor 784.1
Rank \( 1 \)

Related objects

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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 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
784.1-c1 \( \bigl[a\) , \( 0\) , \( a\) , \( -1\) , \( 0\bigr] \)
784.1-c2 \( \bigl[a\) , \( 0\) , \( a\) , \( 50 a - 91\) , \( -274 a + 370\bigr] \)
784.1-c3 \( \bigl[a\) , \( 0\) , \( a\) , \( -11\) , \( 10\bigr] \)
784.1-c4 \( \bigl[a\) , \( 0\) , \( a\) , \( -50 a - 91\) , \( 274 a + 370\bigr] \)

Rank

Rank: \( 1 \)

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