Properties

Base field \(\Q(\sqrt{57}) \)
Label 2.2.57.1-225.1-b
Conductor 225.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{57}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 14 \); class number \(1\).

Elliptic curves in class 225.1-b over \(\Q(\sqrt{57}) \)

Isogeny class 225.1-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
225.1-b1 \( \bigl[1\) , \( a\) , \( 0\) , \( 13203 a - 56436\) , \( 2999025 a - 12820581\bigr] \)
225.1-b2 \( \bigl[1\) , \( a\) , \( 0\) , \( 3 a - 6\) , \( -675 a + 2889\bigr] \)
225.1-b3 \( \bigl[1\) , \( a\) , \( 0\) , \( -4197 a + 17949\) , \( 157371 a - 672744\bigr] \)
225.1-b4 \( \bigl[1\) , \( a\) , \( 0\) , \( 1203 a - 5136\) , \( 19185 a - 82011\bigr] \)
225.1-b5 \( \bigl[1\) , \( a\) , \( 0\) , \( 603 a - 2571\) , \( -16029 a + 68526\bigr] \)
225.1-b6 \( \bigl[1\) , \( a\) , \( 0\) , \( 16203 a - 69261\) , \( 2163735 a - 9249786\bigr] \)
225.1-b7 \( \bigl[1\) , \( a\) , \( 0\) , \( 9603 a - 41046\) , \( -1004859 a + 4295691\bigr] \)
225.1-b8 \( \bigl[1\) , \( a\) , \( 0\) , \( 259203 a - 1108086\) , \( 139305645 a - 595520091\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph