Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-676.4-d
Conductor 676.4
Rank \( 1 \)

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 676.4-d over \(\Q(\sqrt{17}) \)

Isogeny class 676.4-d contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
676.4-d1 \( \bigl[1\) , \( -a - 1\) , \( a\) , \( -9 a - 14\) , \( 8 a + 12\bigr] \)
676.4-d2 \( \bigl[1\) , \( a - 1\) , \( a\) , \( -3\) , \( -7 a + 13\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph