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

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

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

Curve label	Weierstrass Coefficients
28.1-e1	\( \bigl[1\) , \( 1\) , \( a\) , \( -3542109 a + 27860313\) , \( -1427729802 a + 11229751535\bigr] \)
28.1-e2	\( \bigl[1\) , \( 1\) , \( a\) , \( 465128408 a + 3193320452\) , \( 105260041428379 a + 722658596796462\bigr] \)
28.1-e3	\( \bigl[1\) , \( 1\) , \( a\) , \( -34459453116854 a - 236579994629237\) , \( 284797544467916034746 a + 1955266130085115360967\bigr] \)
28.1-e4	\( \bigl[1\) , \( 1\) , \( a\) , \( 293 a - 2308\) , \( -941 a + 7386\bigr] \)

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