Properties

Base field \(\Q(\sqrt{29}) \)
Label 2.2.29.1-196.2-b
Conductor 196.2
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{29}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 7 \); class number \(1\).

Elliptic curves in class 196.2-b over \(\Q(\sqrt{29}) \)

Isogeny class 196.2-b contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
196.2-b1 \( \bigl[1\) , \( 1\) , \( a + 1\) , \( 50 a - 162\) , \( -306 a + 972\bigr] \)
196.2-b2 \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -310 a + 993\) , \( 12459 a - 39768\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph