Properties

Base field \(\Q(\sqrt{165}) \)
Label 2.2.165.1-15.1-f
Conductor 15.1
Rank not recorded

Related objects

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Base field \(\Q(\sqrt{165}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 41 \); class number \(2\).

Elliptic curves in class 15.1-f over \(\Q(\sqrt{165}) \)

Isogeny class 15.1-f contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
15.1-f1 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 12867 a - 89067\) , \( 3850257 a - 26653866\bigr] \)
15.1-f2 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -3 a + 33\) , \( -843 a + 5844\bigr] \)
15.1-f3 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -4098 a + 28383\) , \( 170895 a - 1183029\bigr] \)
15.1-f4 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 1167 a - 8067\) , \( 31737 a - 219696\bigr] \)
15.1-f5 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 582 a - 4017\) , \( -16305 a + 112881\bigr] \)
15.1-f6 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 15792 a - 109317\) , \( 2820387 a - 19524471\bigr] \)
15.1-f7 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 9357 a - 64767\) , \( -1200795 a + 8312646\bigr] \)
15.1-f8 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 252717 a - 1749567\) , \( 176592117 a - 1222480176\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph