Properties

Base field \(\Q(\sqrt{7}) \)
Label 2.2.28.1-63.1-b
Conductor 63.1
Rank not recorded

Related objects

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

Generator \(a\), with minimal polynomial \( x^{2} - 7 \); class number \(1\).

Elliptic curves in class 63.1-b over \(\Q(\sqrt{7}) \)

Isogeny class 63.1-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
63.1-b1 \( \bigl[a\) , \( 1\) , \( a\) , \( -35\) , \( 182\bigr] \)
63.1-b2 \( \bigl[a\) , \( 1\) , \( a\) , \( 115 a - 320\) , \( 1198 a - 3392\bigr] \)
63.1-b3 \( \bigl[a\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \)
63.1-b4 \( \bigl[a\) , \( 1\) , \( a\) , \( -5\) , \( -4\bigr] \)
63.1-b5 \( \bigl[a\) , \( 1\) , \( a\) , \( -40\) , \( -130\bigr] \)
63.1-b6 \( \bigl[a\) , \( 1\) , \( a\) , \( -50\) , \( 86\bigr] \)
63.1-b7 \( \bigl[a\) , \( 1\) , \( a\) , \( -115 a - 320\) , \( -1198 a - 3392\bigr] \)
63.1-b8 \( \bigl[a\) , \( 1\) , \( a\) , \( -785\) , \( 7730\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph