Elliptic curve isogeny class 2028.1-b over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-2028.1-b
• Conductor: 2028.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 2028.1-b over \(\Q(\sqrt{21}) \)

Isogeny class 2028.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
2028.1-b1	\( \bigl[1\) , \( 1\) , \( 0\) , \( -19\) , \( 685\bigr] \)
2028.1-b2	\( \bigl[1\) , \( 1\) , \( 0\) , \( -2339\) , \( -15747\bigr] \)
2028.1-b3	\( \bigl[1\) , \( 1\) , \( 0\) , \( -1299\) , \( 17325\bigr] \)
2028.1-b4	\( \bigl[1\) , \( 1\) , \( 0\) , \( -20739\) , \( 1140957\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph