Properties

Base field \(\Q(\sqrt{51}) \)
Label 2.2.204.1-17.1-d
Conductor 17.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{51}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 51 \); class number \(2\).

Elliptic curves in class 17.1-d over \(\Q(\sqrt{51}) \)

Isogeny class 17.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
17.1-d1 \( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( -14\bigr] \)
17.1-d2 \( \bigl[1\) , \( -1\) , \( 1\) , \( -1\) , \( 0\bigr] \)
17.1-d3 \( \bigl[1\) , \( -1\) , \( 1\) , \( -6\) , \( -4\bigr] \)
17.1-d4 \( \bigl[1\) , \( -1\) , \( 1\) , \( -91\) , \( -310\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph