Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-12482.1-d
Conductor 12482.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{-2}) \)

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

Elliptic curves in class 12482.1-d over \(\Q(\sqrt{-2}) \)

Isogeny class 12482.1-d contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
12482.1-d1 \( \bigl[1\) , \( 1\) , \( 1\) , \( -420\) , \( 3109\bigr] \)
12482.1-d2 \( \bigl[1\) , \( 1\) , \( 1\) , \( -23380\) , \( -1385691\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph