Elliptic curve isogeny class 24.1-b over number field \(\Q(\sqrt{51}) \)

• Base field: \(\Q(\sqrt{51}) \)
• Label: 2.2.204.1-24.1-b
• Conductor: 24.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 24.1-b over \(\Q(\sqrt{51}) \)

Isogeny class 24.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
24.1-b1	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -2746 a + 19640\) , \( -1543982 a + 11026268\bigr] \)
24.1-b2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
24.1-b3	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -754 a - 5355\) , \( -26862 a - 191802\bigr] \)
24.1-b4	\( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 4254 a - 30350\) , \( -362098 a + 2585928\bigr] \)
24.1-b5	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -11254 a - 80340\) , \( -1799688 a - 12852312\bigr] \)
24.1-b6	\( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -67254 a - 480260\) , \( 25001614 a + 178547268\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph