Properties

Base field \(\Q(\sqrt{114}) \)
Label 2.2.456.1-2.1-d
Conductor 2.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{114}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 114 \); class number \(2\).

Elliptic curves in class 2.1-d over \(\Q(\sqrt{114}) \)

Isogeny class 2.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
2.1-d1 \( \bigl[1\) , \( -1\) , \( 1\) , \( -4068 a - 43435\) , \( -472750 a - 5047589\bigr] \)
2.1-d2 \( \bigl[1\) , \( -1\) , \( 1\) , \( -258 a - 2755\) , \( -7114 a - 75957\bigr] \)
2.1-d3 \( \bigl[1\) , \( -1\) , \( 1\) , \( -4098 a - 43755\) , \( -465578 a - 4971013\bigr] \)
2.1-d4 \( \bigl[1\) , \( -1\) , \( 1\) , \( -65568 a - 700075\) , \( -29846182 a - 318670021\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph