Properties

Base field \(\Q(\sqrt{77}) \)
Label 2.2.77.1-175.1-a
Conductor 175.1
Rank \( 1 \)

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

Isogeny class 175.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
175.1-a1 \( \bigl[0\) , \( a + 1\) , \( 1\) , \( 1183 a - 5772\) , \( -49618 a + 242512\bigr] \)
175.1-a2 \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -11 a - 40\) , \( -30 a - 116\bigr] \)
175.1-a3 \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 79 a + 310\) , \( -20 a - 77\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph