Properties

Base field \(\Q(\sqrt{17}) \)
Label 2.2.17.1-612.1-c
Conductor 612.1
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 612.1-c over \(\Q(\sqrt{17}) \)

Isogeny class 612.1-c contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
612.1-c1 \( \bigl[1\) , \( a\) , \( 1\) , \( -7 a - 11\) , \( 857 a + 1338\bigr] \)
612.1-c2 \( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -6 a - 7\) , \( 12 a + 21\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph