Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-400.4-c
Conductor 400.4
Rank \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 400.4-c over \(\Q(\sqrt{17}) \)

Isogeny class 400.4-c contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
400.4-c1 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -1\) , \( 3 a + 4\bigr] \)
400.4-c2 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -a\) , \( a - 4\bigr] \)