Elliptic curve isogeny class 65.3-b over number field \(\Q(\sqrt{-51}) \)

• Base field: \(\Q(\sqrt{-51}) \)
• Label: 2.0.51.1-65.3-b
• Conductor: 65.3
• Rank: \( 0 \)

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

Generator \(a\), with minimal polynomial \( x^{2} - x + 13 \); class number \(2\).

Elliptic curves in class 65.3-b over \(\Q(\sqrt{-51}) \)

Isogeny class 65.3-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
65.3-b1	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 48 a - 624\) , \( 771 a - 5204\bigr] \)
65.3-b2	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -42 a - 174\) , \( 465 a + 592\bigr] \)
65.3-b3	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 3 a + 6\) , \( -3 a - 11\bigr] \)
65.3-b4	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 3 a - 39\) , \( 24 a - 56\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph