Properties

Base field \(\Q(\sqrt{77}) \)
Label 2.2.77.1-63.1-a
Conductor 63.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{77}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 19 \); class number \(1\).

Elliptic curves in class 63.1-a over \(\Q(\sqrt{77}) \)

Isogeny class 63.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
63.1-a1 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -307 a - 1182\) , \( 16747 a + 65111\bigr] \)
63.1-a2 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 8 a + 43\) , \( 17 a + 74\bigr] \)
63.1-a3 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -37 a - 132\) , \( 7 a + 35\bigr] \)
63.1-a4 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -352 a - 1357\) , \( -7903 a - 30716\bigr] \)
63.1-a5 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -442 a - 1707\) , \( 9997 a + 38870\bigr] \)
63.1-a6 \( \bigl[a\) , \( 0\) , \( 0\) , \( 7057 a - 34489\) , \( -667087 a + 3260376\bigr] \)

Rank

Rank: \( 0 \)

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