Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-2450.1-d
Conductor 2450.1
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 2450.1-d over \(\Q(\sqrt{2}) \)

Isogeny class 2450.1-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
2450.1-d1 \( \bigl[1\) , \( a\) , \( 1\) , \( 2849 a - 2615\) , \( -68114 a + 114698\bigr] \)
2450.1-d2 \( \bigl[1\) , \( a\) , \( 1\) , \( -21 a - 445\) , \( -410 a + 2838\bigr] \)
2450.1-d3 \( \bigl[1\) , \( a\) , \( 1\) , \( -971 a - 1795\) , \( -25410 a - 32622\bigr] \)
2450.1-d4 \( \bigl[1\) , \( a\) , \( 1\) , \( -141 a - 225\) , \( 1086 a + 1598\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph