Elliptic curve isogeny class 49.1-b over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-49.1-b
• Conductor: 49.1
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 7 & 2 & 14 \\ 7 & 1 & 14 & 2 \\ 2 & 14 & 1 & 7 \\ 14 & 2 & 7 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 49.1-b over \(\Q(\sqrt{21}) \)

Isogeny class 49.1-b contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
49.1-b1	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 10 a - 28\) , \( -24 a + 67\bigr] \)
49.1-b2	\( \bigl[1\) , \( -1\) , \( 0\) , \( -2\) , \( -1\bigr] \)
49.1-b3	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 185 a - 518\) , \( -1872 a + 5226\bigr] \)
49.1-b4	\( \bigl[1\) , \( -1\) , \( 0\) , \( -37\) , \( -78\bigr] \)