Properties

Base field \(\Q(\sqrt{65}) \)
Label 2.2.65.1-100.1-h
Conductor 100.1
Rank \( 1 \)

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 100.1-h over \(\Q(\sqrt{65}) \)

Isogeny class 100.1-h contains 4 curves linked by isogenies of degrees dividing 15.

Curve label Weierstrass Coefficients
100.1-h1 \( \bigl[1\) , \( 0\) , \( 1\) , \( -126\) , \( -552\bigr] \)
100.1-h2 \( \bigl[a\) , \( a + 1\) , \( a\) , \( -23 a - 88\) , \( 96 a + 336\bigr] \)
100.1-h3 \( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( -2\bigr] \)
100.1-h4 \( \bigl[a\) , \( a + 1\) , \( a\) , \( 202 a + 712\) , \( -674 a - 2384\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph