Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-2450.3-h
Conductor 2450.3
Rank \( 0 \)

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 2450.3-h over \(\Q(\sqrt{2}) \)

Isogeny class 2450.3-h contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
2450.3-h1 \( \bigl[1\) , \( -1\) , \( 1\) , \( -7 a - 13\) , \( -15 a - 21\bigr] \)
2450.3-h2 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -136 a + 184\) , \( 174 a - 270\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph