Properties

Base field \(\Q(\sqrt{77}) \)
Label 2.2.77.1-44.1-c
Conductor 44.1
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 44.1-c over \(\Q(\sqrt{77}) \)

Isogeny class 44.1-c contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
44.1-c1 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -4 a + 5\) , \( -3 a + 7\bigr] \)
44.1-c2 \( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( 6 a - 45\) , \( 23 a - 121\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph