Properties

Base field \(\Q(\sqrt{46}) \)
Label 2.2.184.1-32.1-b
Conductor 32.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{46}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 46 \); class number \(1\).

Elliptic curves in class 32.1-b over \(\Q(\sqrt{46}) \)

Isogeny class 32.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
32.1-b1 \( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \)
32.1-b2 \( \bigl[0\) , \( 0\) , \( 0\) , \( 174627960 a + 1184384449\) , \( 0\bigr] \)
32.1-b3 \( \bigl[a\) , \( -1\) , \( 0\) , \( -480226890 a - 3257057198\) , \( -14875180710936 a - 100888384140145\bigr] \)
32.1-b4 \( \bigl[a\) , \( -1\) , \( a\) , \( -480226890 a - 3257057221\) , \( 14871819122706 a + 100865584739576\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph