Properties

Base field \(\Q(\sqrt{77}) \)
Label 2.2.77.1-7.1-b
Conductor 7.1
Rank not recorded

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 7.1-b over \(\Q(\sqrt{77}) \)

Isogeny class 7.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
7.1-b1 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -3 a + 4\) , \( -2 a + 4\bigr] \)
7.1-b2 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 2 a - 21\) , \( 26 a - 133\bigr] \)
7.1-b3 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 422 a - 2086\) , \( 11275 a - 55139\bigr] \)
7.1-b4 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( 22 a - 131\) , \( 228 a - 1147\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 6 & 3 \\ 2 & 1 & 3 & 6 \\ 6 & 3 & 1 & 2 \\ 3 & 6 & 2 & 1 \end{array}\right)\)

Isogeny graph