Properties

Base field \(\Q(\sqrt{217}) \)
Label 2.2.217.1-4.1-b
Conductor 4.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{217}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 54 \); class number \(1\).

Elliptic curves in class 4.1-b over \(\Q(\sqrt{217}) \)

Isogeny class 4.1-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
4.1-b1 \( \bigl[1\) , \( 0\) , \( 0\) , \( -5894 a - 40465\) , \( 851278 a + 5844415\bigr] \)
4.1-b2 \( \bigl[1\) , \( 0\) , \( 0\) , \( 5894 a - 46359\) , \( -851278 a + 6695693\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph