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

• Base field: \(\Q(\sqrt{217}) \)
• Label: 2.2.217.1-28.1-g
• 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-g over \(\Q(\sqrt{217}) \)

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

Curve label	Weierstrass Coefficients
28.1-g1	\( \bigl[1\) , \( 0\) , \( a\) , \( -3215 a - 22069\) , \( 296627 a + 2036469\bigr] \)
28.1-g2	\( \bigl[1\) , \( 0\) , \( a\) , \( 301954 a - 2375011\) , \( -1763011435 a + 13866895785\bigr] \)
28.1-g3	\( \bigl[1\) , \( 0\) , \( a\) , \( 33477944960 a - 263319434670\) , \( -9004819170532378 a + 70827044374677700\bigr] \)
28.1-g4	\( \bigl[1\) , \( 0\) , \( a\) , \( -a - 12\) , \( 2 a - 8\bigr] \)

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