Elliptic curve isogeny class 28.1-b over number field \(\Q(\sqrt{217}) \)

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

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

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

Elliptic curves in class 28.1-b over \(\Q(\sqrt{217}) \)

Isogeny class 28.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
28.1-b1	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -465128409 a + 3658448860\) , \( -105260041428380 a + 827918638224841\bigr] \)
28.1-b2	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 3542108 a + 24318204\) , \( 1427729801 a + 9802021733\bigr] \)
28.1-b3	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -294 a - 2015\) , \( 940 a + 6445\bigr] \)
28.1-b4	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( 34459453116853 a - 271039447746091\) , \( -284797544467916034747 a + 2240063674553031395713\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph