Properties

Base field \(\Q(\sqrt{165}) \)
Label 2.2.165.1-33.1-c
Conductor 33.1
Rank \( 0 \)

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 33.1-c over \(\Q(\sqrt{165}) \)

Isogeny class 33.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
33.1-c1 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -557 a + 3963\) , \( 5853 a - 40304\bigr] \)
33.1-c2 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 158 a - 987\) , \( 903 a - 6039\bigr] \)
33.1-c3 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 93 a - 537\) , \( -999 a + 7128\bigr] \)
33.1-c4 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( 1913 a - 13137\) , \( 115761 a - 801162\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph