Properties

Base field \(\Q(\sqrt{77}) \)
Label 2.2.77.1-77.1-j
Conductor 77.1
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 77.1-j over \(\Q(\sqrt{77}) \)

Isogeny class 77.1-j contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
77.1-j1 \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -803 a - 3120\) , \( -24422 a - 94941\bigr] \)
77.1-j2 \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -443 a - 1720\) , \( -48462 a - 188396\bigr] \)
77.1-j3 \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 3967 a + 15430\) , \( 1269148 a + 4933819\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph