Elliptic curve isogeny class 7.1-b over number field \(\Q(\sqrt{217}) \)

• Base field: \(\Q(\sqrt{217}) \)
• Label: 2.2.217.1-7.1-b
• Conductor: 7.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 7.1-b over \(\Q(\sqrt{217}) \)

Isogeny class 7.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
7.1-b1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -945951 a - 6494389\) , \( 23919915394 a + 164221220698\bigr] \)
7.1-b2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -129 a - 886\) , \( -656 a - 4504\bigr] \)
7.1-b3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -3555471 a - 24409944\) , \( 9820546524 a + 67422568664\bigr] \)
7.1-b4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -173213478909 a - 1189190199016\) , \( 106496592842533228 a + 731148090983376684\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph