Elliptic curve isogeny class 1452.1-b over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1452.1-b
• Conductor: 1452.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{21}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 5 \); class number \(1\).

Elliptic curves in class 1452.1-b over \(\Q(\sqrt{21}) \)

Isogeny class 1452.1-b contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
1452.1-b1	\( \bigl[a\) , \( 1\) , \( a\) , \( 50275 a - 140771\) , \( -9317141 a + 26009932\bigr] \)
1452.1-b2	\( \bigl[a\) , \( 1\) , \( a\) , \( -575 a + 1609\) , \( 12889 a - 35978\bigr] \)
1452.1-b3	\( \bigl[a\) , \( 1\) , \( a\) , \( 225 a - 631\) , \( 2169 a - 6058\bigr] \)
1452.1-b4	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -50327 a - 90586\) , \( 9297650 a + 16657871\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph