Properties

Base field \(\Q(\sqrt{77}) \)
Label 2.2.77.1-121.1-e
Conductor 121.1
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 121.1-e over \(\Q(\sqrt{77}) \)

Isogeny class 121.1-e contains 2 curves linked by isogenies of degree 11.

Curve label Weierstrass Coefficients
121.1-e1 \( \bigl[1\) , \( 1\) , \( 1\) , \( -30\) , \( -76\bigr] \)
121.1-e2 \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -18 a - 73\) , \( 395 a + 1531\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph