Properties

Base field \(\Q(\sqrt{-7}) \)
Label 2.0.7.1-44800.5-n
Conductor 44800.5
Rank \( 1 \)

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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 44800.5-n over \(\Q(\sqrt{-7}) \)

Isogeny class 44800.5-n contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
44800.5-n1 \( \bigl[0\) , \( 0\) , \( 0\) , \( -96 a - 11\) , \( 480 a - 326\bigr] \)
44800.5-n2 \( \bigl[0\) , \( 0\) , \( 0\) , \( 96 a - 107\) , \( -480 a + 154\bigr] \)
44800.5-n3 \( \bigl[0\) , \( 0\) , \( 0\) , \( 37\) , \( 138\bigr] \)
44800.5-n4 \( \bigl[0\) , \( 0\) , \( 0\) , \( -283\) , \( 1482\bigr] \)
44800.5-n5 \( \bigl[0\) , \( 0\) , \( 0\) , \( -1403\) , \( -18902\bigr] \)
44800.5-n6 \( \bigl[0\) , \( 0\) , \( 0\) , \( -4283\) , \( 107882\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph