Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-578.3-d
Conductor 578.3
Rank \( 0 \)

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 578.3-d over \(\Q(\sqrt{2}) \)

Isogeny class 578.3-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
578.3-d1 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -19 a + 5\) , \( -32 a - 19\bigr] \)
578.3-d2 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 201 a - 210\) , \( -1560 a + 2026\bigr] \)
578.3-d3 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 2681 a - 4210\) , \( -97352 a + 135050\bigr] \)
578.3-d4 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( -89 a - 255\) , \( -1158 a - 1559\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph