Properties

Base field \(\Q(\sqrt{23}) \)
Label 2.2.92.1-64.1-a
Conductor 64.1
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 64.1-a over \(\Q(\sqrt{23}) \)

Isogeny class 64.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
64.1-a1 \( \bigl[0\) , \( 0\) , \( 0\) , \( -1\) , \( 0\bigr] \)
64.1-a2 \( \bigl[0\) , \( 0\) , \( 0\) , \( -240 a + 1151\) , \( 0\bigr] \)
64.1-a3 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 665 a - 3148\) , \( 19897 a - 95346\bigr] \)
64.1-a4 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 666 a - 3136\) , \( -20405 a + 97944\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph