Properties

Base field \(\Q(\sqrt{23}) \)
Label 2.2.92.1-100.1-f
Conductor 100.1
Rank \( 0 \)

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 100.1-f over \(\Q(\sqrt{23}) \)

Isogeny class 100.1-f contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
100.1-f1 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 2178 a - 10441\) , \( -178033 a + 853818\bigr] \)
100.1-f2 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -222 a + 1069\) , \( 3327 a - 15954\bigr] \)
100.1-f3 \( \bigl[0\) , \( -1\) , \( 0\) , \( -1\) , \( 0\bigr] \)
100.1-f4 \( \bigl[0\) , \( -1\) , \( 0\) , \( -41\) , \( 116\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph