Elliptic curve isogeny class 100.1-b over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-100.1-b
• Conductor: 100.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 100.1-b over \(\Q(\sqrt{21}) \)

Isogeny class 100.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
100.1-b1	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -2 a - 3\) , \( 4 a + 7\bigr] \)
100.1-b2	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -12 a - 23\) , \( -22 a - 39\bigr] \)
100.1-b3	\( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -62 a - 118\) , \( -345 a - 629\bigr] \)
100.1-b4	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 925 a - 2591\) , \( 19888 a - 55537\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph