Elliptic curve isogeny class 4.1-d over number field \(\Q(\sqrt{217}) \)

• Base field: \(\Q(\sqrt{217}) \)
• Label: 2.2.217.1-4.1-d
• Conductor: 4.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 4.1-d over \(\Q(\sqrt{217}) \)

Isogeny class 4.1-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
4.1-d1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -76876685 a - 527793801\) , \( -996242529392 a - 6839663167426\bigr] \)
4.1-d2	\( \bigl[1\) , \( 0\) , \( 1\) , \( 76876685 a - 604670486\) , \( 996242529392 a - 7835905696818\bigr] \)
4.1-d3	\( \bigl[1\) , \( 0\) , \( 1\) , \( 1230190055 a - 9676010586\) , \( 63741468271084 a - 501355964650234\bigr] \)
4.1-d4	\( \bigl[1\) , \( 0\) , \( 1\) , \( -1230190055 a - 8445820531\) , \( -63741468271084 a - 437614496379150\bigr] \)

Rank

Rank: \( 0 \)

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