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

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

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

Curve label	Weierstrass Coefficients
28.1-d1	\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -301955 a - 2073057\) , \( 1763011434 a + 12103884350\bigr] \)
28.1-d2	\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 3214 a - 25284\) , \( -296628 a + 2333096\bigr] \)
28.1-d3	\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -13\) , \( -3 a - 6\bigr] \)
28.1-d4	\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -33477944961 a - 229841489710\) , \( 9004819170532377 a + 61822225204145322\bigr] \)

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