Properties

Base field \(\Q(\sqrt{217}) \)
Label 2.2.217.1-28.1-a
Conductor 28.1
Rank \( 1 \)

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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 28.1-a over \(\Q(\sqrt{217}) \)

Isogeny class 28.1-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
28.1-a1 \( \bigl[1\) , \( 1\) , \( 0\) , \( -684208655873630 a - 4697407111568275\) , \( 26515386059767548453800 a + 182040320557030242023013\bigr] \)
28.1-a2 \( \bigl[1\) , \( 1\) , \( 0\) , \( 2089824849950 a - 16437433620775\) , \( 9033133540492898000 a - 71049749917082986023\bigr] \)
28.1-a3 \( \bigl[1\) , \( 1\) , \( 0\) , \( -17972493709570 a + 141361929138670\) , \( -188910303755554419300 a + 1485866424804336914156\bigr] \)
28.1-a4 \( \bigl[1\) , \( 1\) , \( 0\) , \( -142526054766590 a - 978506918170300\) , \( 2060375383192230440900 a + 14145424636801074551712\bigr] \)
28.1-a5 \( \bigl[1\) , \( 1\) , \( 0\) , \( 42214461968990 a - 332036159139665\) , \( 404920008132587532600 a - 3184882099359922786381\bigr] \)
28.1-a6 \( \bigl[1\) , \( 1\) , \( 0\) , \( 10956115758347870 a - 86174889500277745\) , \( -1694134786000379256716200 a + 13325149277555118368887821\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph