Properties

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

Isogeny class 2450.1-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
2450.1-a1 \( \bigl[1\) , \( a - 1\) , \( a\) , \( 8 a - 24\) , \( -36 a + 64\bigr] \)
2450.1-a2 \( \bigl[1\) , \( a - 1\) , \( a\) , \( 1628 a - 2404\) , \( 42084 a - 61450\bigr] \)
2450.1-a3 \( \bigl[1\) , \( a - 1\) , \( a\) , \( 28 a - 29\) , \( 39 a + 15\bigr] \)
2450.1-a4 \( \bigl[1\) , \( a - 1\) , \( a\) , \( -162 a + 31\) , \( 649 a + 39\bigr] \)
2450.1-a5 \( \bigl[1\) , \( a - 1\) , \( a\) , \( 588 a - 3844\) , \( 20724 a - 93386\bigr] \)
2450.1-a6 \( \bigl[1\) , \( a - 1\) , \( a\) , \( -57 a - 114\) , \( 309 a + 560\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph