Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-441.3-d
Conductor 441.3
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 441.3-d over \(\Q(\sqrt{2}) \)

Isogeny class 441.3-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
441.3-d1 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 101 a - 74\) , \( -277 a + 221\bigr] \)
441.3-d2 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 26 a - 59\) , \( 134 a - 214\bigr] \)
441.3-d3 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -4 a - 4\) , \( 10 a - 3\bigr] \)
441.3-d4 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 431 a - 924\) , \( 7681 a - 13013\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph