Properties

Base field \(\Q(\sqrt{77}) \)
Label 2.2.77.1-99.1-b
Conductor 99.1
Rank \( 0 \)

Related objects

Learn more

Base field \(\Q(\sqrt{77}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 19 \); class number \(1\).

Elliptic curves in class 99.1-b over \(\Q(\sqrt{77}) \)

Isogeny class 99.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
99.1-b1 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( -386 a + 1934\) , \( 2836 a - 13797\bigr] \)
99.1-b2 \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -99 a - 388\) , \( -804 a - 3130\bigr] \)
99.1-b3 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 64 a - 266\) , \( -484 a + 2427\bigr] \)
99.1-b4 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 1324 a - 6426\) , \( 54956 a - 268543\bigr] \)

Rank

Rank: \( 0 \)

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