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

• Base field: \(\Q(\sqrt{51}) \)
• Label: 2.2.204.1-17.1-b
• Conductor: 17.1
• Rank: \( 2 \)

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

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

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

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

Curve label	Weierstrass Coefficients
17.1-b1	\( \bigl[a\) , \( 0\) , \( 0\) , \( 48\) , \( -325\bigr] \)
17.1-b2	\( \bigl[a\) , \( 0\) , \( 0\) , \( 48\) , \( 53\bigr] \)
17.1-b3	\( \bigl[a\) , \( 0\) , \( 0\) , \( 3\) , \( -280\bigr] \)
17.1-b4	\( \bigl[a\) , \( 0\) , \( 0\) , \( -762\) , \( -12367\bigr] \)

Rank

Rank: \( 2 \)

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