Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-7056.3-c
Conductor 7056.3
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 7056.3-c over \(\Q(\sqrt{-2}) \)

Isogeny class 7056.3-c contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
7056.3-c1 \( \bigl[a\) , \( -a\) , \( 0\) , \( 82 a - 160\) , \( -568 a + 708\bigr] \)
7056.3-c2 \( \bigl[a\) , \( -a\) , \( a\) , \( -27 a + 43\) , \( 8 a + 155\bigr] \)
7056.3-c3 \( \bigl[a\) , \( -a\) , \( 0\) , \( 68 a + 76\) , \( -120 a + 536\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph