Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-5202.4-c
Conductor 5202.4
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 5202.4-c over \(\Q(\sqrt{-2}) \)

Isogeny class 5202.4-c contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
5202.4-c1 \( \bigl[a + 1\) , \( a\) , \( a\) , \( -44 a + 477\) , \( -4395 a + 1929\bigr] \)
5202.4-c2 \( \bigl[a + 1\) , \( a\) , \( a\) , \( -4 a - 8\) , \( -8 a - 2\bigr] \)
5202.4-c3 \( \bigl[a + 1\) , \( a\) , \( a\) , \( -19 a - 28\) , \( 41 a + 52\bigr] \)
5202.4-c4 \( \bigl[a + 1\) , \( a\) , \( a\) , \( 16 a + 557\) , \( -3303 a + 257\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 10 & 5 & 2 \\ 10 & 1 & 2 & 5 \\ 5 & 2 & 1 & 10 \\ 2 & 5 & 10 & 1 \end{array}\right)\)

Isogeny graph