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

• Base field: \(\Q(\sqrt{217}) \)
• Label: 2.2.217.1-7.1-a
• 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-a over \(\Q(\sqrt{217}) \)

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

Curve label	Weierstrass Coefficients
7.1-a1	\( \bigl[1\) , \( -1\) , \( 1\) , \( 945951 a - 7440340\) , \( -23919915394 a + 188141136092\bigr] \)
7.1-a2	\( \bigl[1\) , \( -1\) , \( 1\) , \( 173213478909 a - 1362403677925\) , \( -106496592842533228 a + 837644683825909912\bigr] \)
7.1-a3	\( \bigl[1\) , \( -1\) , \( 1\) , \( 3555471 a - 27965415\) , \( -9820546524 a + 77243115188\bigr] \)
7.1-a4	\( \bigl[1\) , \( -1\) , \( 1\) , \( 129 a - 1015\) , \( 656 a - 5160\bigr] \)

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