Properties

Base field \(\Q(\sqrt{77}) \)
Label 2.2.77.1-275.1-a
Conductor 275.1
Rank not recorded

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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 275.1-a over \(\Q(\sqrt{77}) \)

Isogeny class 275.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
275.1-a1 \( \bigl[1\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
275.1-a2 \( \bigl[1\) , \( -1\) , \( 0\) , \( -4\) , \( 3\bigr] \)
275.1-a3 \( \bigl[1\) , \( -1\) , \( 0\) , \( -29\) , \( -52\bigr] \)
275.1-a4 \( \bigl[1\) , \( -1\) , \( 0\) , \( -59\) , \( 190\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph