Properties

Base field \(\Q(\sqrt{34}) \)
Label 2.2.136.1-18.1-b
Conductor 18.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{34}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 34 \); class number \(2\).

Elliptic curves in class 18.1-b over \(\Q(\sqrt{34}) \)

Isogeny class 18.1-b contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
18.1-b1 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 573 a - 3311\) , \( 24049 a - 140165\bigr] \)
18.1-b2 \( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 3708 a - 21591\) , \( -2114775 a + 12331215\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph