Properties

Base field \(\Q(\sqrt{26}) \)
Label 2.2.104.1-17.1-b
Conductor 17.1
Rank \( 2 \)

Related objects

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Base field \(\Q(\sqrt{26}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 26 \); class number \(2\).

Elliptic curves in class 17.1-b over \(\Q(\sqrt{26}) \)

Isogeny class 17.1-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
17.1-b1 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 8 a - 6\) , \( -3 a + 53\bigr] \)
17.1-b2 \( \bigl[a + 1\) , \( 1\) , \( 0\) , \( 3 a + 19\) , \( 4 a + 16\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph