Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-10404.2-c
Conductor 10404.2
Rank not recorded

Related objects

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Base field \(\Q(\sqrt{-7}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 2 \); class number \(1\).

Elliptic curves in class 10404.2-c over \(\Q(\sqrt{-7}) \)

Isogeny class 10404.2-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
10404.2-c1 \( \bigl[1\) , \( 0\) , \( 0\) , \( -1644\) , \( -30942\bigr] \)
10404.2-c2 \( \bigl[1\) , \( 0\) , \( 0\) , \( 226\) , \( -2232\bigr] \)
10404.2-c3 \( \bigl[1\) , \( 0\) , \( 0\) , \( -114\) , \( -396\bigr] \)
10404.2-c4 \( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( 68\bigr] \)
10404.2-c5 \( \bigl[1\) , \( 0\) , \( 0\) , \( -1734\) , \( -27936\bigr] \)
10404.2-c6 \( \bigl[1\) , \( 0\) , \( 0\) , \( -27744\) , \( -1781010\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph