Properties

Base field \(\Q(\sqrt{23}) \)
Label 2.2.92.1-9.1-a
Conductor 9.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{23}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 23 \); class number \(1\).

Elliptic curves in class 9.1-a over \(\Q(\sqrt{23}) \)

Isogeny class 9.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
9.1-a1 \( \bigl[1\) , \( 0\) , \( 0\) , \( 715 a - 3429\) , \( -23270 a + 111599\bigr] \)
9.1-a2 \( \bigl[a\) , \( 0\) , \( 0\) , \( -11590 a - 55573\) , \( -1475005 a - 7073869\bigr] \)
9.1-a3 \( \bigl[1\) , \( 0\) , \( 0\) , \( 11515 a - 55224\) , \( -1472000 a + 7059464\bigr] \)
9.1-a4 \( \bigl[1\) , \( 0\) , \( 0\) , \( 11590 a - 55584\) , \( -1451825 a + 6962708\bigr] \)

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