Elliptic curve isogeny class 17.1-a over number field \(\Q(\sqrt{51}) \)

• Base field: \(\Q(\sqrt{51}) \)
• Label: 2.2.204.1-17.1-a
• Conductor: 17.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{51}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 51 \); class number \(2\).

Elliptic curves in class 17.1-a over \(\Q(\sqrt{51}) \)

Isogeny class 17.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
17.1-a1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -6\) , \( 377\bigr] \)
17.1-a2	\( \bigl[1\) , \( -1\) , \( 0\) , \( -6\) , \( -1\bigr] \)
17.1-a3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -51\) , \( 152\bigr] \)
17.1-a4	\( \bigl[1\) , \( -1\) , \( 0\) , \( -816\) , \( 9179\bigr] \)

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