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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1452.1-i
• Conductor: 1452.1
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

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

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

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

Curve label	Weierstrass Coefficients
1452.1-i1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -10055\) , \( -390309\bigr] \)
1452.1-i2	\( \bigl[1\) , \( 0\) , \( 0\) , \( 115\) , \( 561\bigr] \)
1452.1-i3	\( \bigl[1\) , \( 0\) , \( 0\) , \( -45\) , \( 81\bigr] \)
1452.1-i4	\( \bigl[1\) , \( 0\) , \( 0\) , \( -10065\) , \( -389499\bigr] \)