Properties

Base field \(\Q(\sqrt{34}) \)
Label 2.2.136.1-18.3-a
Conductor 18.3
Rank \( 1 \)

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 18.3-a over \(\Q(\sqrt{34}) \)

Isogeny class 18.3-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
18.3-a1 \( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 324 a - 1795\) , \( -7214 a + 42291\bigr] \)
18.3-a2 \( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 29 a - 75\) , \( -87 a + 733\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph