Properties

Base field \(\Q(\sqrt{497}) \)
Label 2.2.497.1-1.1-a
Conductor 1.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{497}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 124 \); class number \(1\).

Elliptic curves in class 1.1-a over \(\Q(\sqrt{497}) \)

Isogeny class 1.1-a contains 4 curves linked by isogenies of degrees dividing 14.

Curve label Weierstrass Coefficients
1.1-a1 \( \bigl[1\) , \( -1\) , \( 0\) , \( 33695 a - 392437\) , \( 13813271 a - 160879692\bigr] \)
1.1-a2 \( \bigl[1\) , \( -1\) , \( 0\) , \( -33695 a - 358742\) , \( -13813271 a - 147066421\bigr] \)
1.1-a3 \( \bigl[1\) , \( -1\) , \( 0\) , \( 572815 a - 6671432\) , \( 787693397 a - 9174066815\bigr] \)
1.1-a4 \( \bigl[1\) , \( -1\) , \( 0\) , \( -572815 a - 6098617\) , \( -787693397 a - 8386373418\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 7 & 2 & 14 \\ 7 & 1 & 14 & 2 \\ 2 & 14 & 1 & 7 \\ 14 & 2 & 7 & 1 \end{array}\right)\)

Isogeny graph