Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-512.2-j
Conductor 512.2
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{17}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 4 \); class number \(1\).

Elliptic curves in class 512.2-j over \(\Q(\sqrt{17}) \)

Isogeny class 512.2-j contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
512.2-j1 \( \bigl[0\) , \( -1\) , \( 0\) , \( 6 a - 15\) , \( 7 a - 18\bigr] \)
512.2-j2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -15 a - 28\) , \( 20 a + 36\bigr] \)
512.2-j3 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -5 a - 8\) , \( -18 a - 28\bigr] \)
512.2-j4 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -95 a - 148\) , \( -848 a - 1324\bigr] \)

Rank

Rank: \( 0 \)

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