Properties

Base field \(\Q(\sqrt{34}) \)
Label 2.2.136.1-18.2-a
Conductor 18.2
Rank \( 1 \)

Related objects

Learn more

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

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

Elliptic curves in class 18.2-a over \(\Q(\sqrt{34}) \)

Isogeny class 18.2-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
18.2-a1 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -10 a - 58\) , \( 12 a + 70\bigr] \)
18.2-a2 \( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -305 a - 1778\) , \( 5419 a + 31598\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph