Properties

Base field \(\Q(\sqrt{6}) \)
Label 2.2.24.1-338.1-e
Conductor 338.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{6}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 6 \); class number \(1\).

Elliptic curves in class 338.1-e over \(\Q(\sqrt{6}) \)

Isogeny class 338.1-e contains 2 curves linked by isogenies of degree 7.

Curve label Weierstrass Coefficients
338.1-e1 \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 4254 a - 10420\) , \( -263508 a + 645460\bigr] \)
338.1-e2 \( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -53 a - 127\) , \( -592 a - 1451\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph