Properties

Base field \(\Q(\sqrt{113}) \)
Label 2.2.113.1-2.1-a
Conductor 2.1
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Base field \(\Q(\sqrt{113}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 28 \); class number \(1\).

Elliptic curves in class 2.1-a over \(\Q(\sqrt{113}) \)

Isogeny class 2.1-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
2.1-a1 \( \bigl[1\) , \( -a\) , \( a + 1\) , \( -57 a - 264\) , \( -14594 a - 70270\bigr] \)
2.1-a2 \( \bigl[1\) , \( -a - 1\) , \( a\) , \( 8\) , \( -a - 8\bigr] \)

Rank

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Isogeny matrix

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

Isogeny graph