Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-1792.5-c
Conductor 1792.5
Rank \( 0 \)

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 1792.5-c over \(\Q(\sqrt{-7}) \)

Isogeny class 1792.5-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
1792.5-c1 \( \bigl[0\) , \( 0\) , \( 0\) , \( 1\) , \( -2\bigr] \)
1792.5-c2 \( \bigl[0\) , \( 0\) , \( 0\) , \( -59\) , \( 138\bigr] \)
1792.5-c3 \( \bigl[0\) , \( 0\) , \( 0\) , \( -19\) , \( -30\bigr] \)
1792.5-c4 \( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a + 7\) , \( -3 a - 4\bigr] \)
1792.5-c5 \( \bigl[0\) , \( 0\) , \( 0\) , \( 3 a + 4\) , \( 3 a - 7\bigr] \)
1792.5-c6 \( \bigl[0\) , \( 0\) , \( 0\) , \( -299\) , \( -1990\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph