Elliptic curve isogeny class 45.1-b over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-45.1-b
• Conductor: 45.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 45.1-b over \(\Q(\sqrt{21}) \)

Isogeny class 45.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
45.1-b1	\( \bigl[a\) , \( a\) , \( 0\) , \( 302 a - 883\) , \( 4418 a - 12272\bigr] \)
45.1-b2	\( \bigl[a\) , \( a\) , \( 0\) , \( 2 a + 2\) , \( -a + 7\bigr] \)
45.1-b3	\( \bigl[a\) , \( a\) , \( 0\) , \( 257 a - 718\) , \( -3487 a + 9718\bigr] \)
45.1-b4	\( \bigl[a\) , \( a\) , \( 0\) , \( 17 a - 43\) , \( -58 a + 163\bigr] \)
45.1-b5	\( \bigl[a\) , \( a\) , \( 0\) , \( 17 a - 88\) , \( 23 a - 8\bigr] \)
45.1-b6	\( \bigl[a\) , \( a\) , \( 0\) , \( -268 a - 13\) , \( 1712 a + 2212\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph