Properties

Base field \(\Q(\sqrt{65}) \)
Label 2.2.65.1-52.1-g
Conductor 52.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{65}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 16 \); class number \(2\).

Elliptic curves in class 52.1-g over \(\Q(\sqrt{65}) \)

Isogeny class 52.1-g contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
52.1-g1 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 834028 a - 3779088\) , \( 834559696 a - 3781497536\bigr] \)
52.1-g2 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 8203 a - 37168\) , \( 1639881 a - 7430512\bigr] \)
52.1-g3 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -872 a + 3952\) , \( -48214 a + 218464\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph