Elliptic curve isogeny class 441.1-c over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-441.1-c
• Conductor: 441.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 441.1-c over \(\Q(\sqrt{21}) \)

Isogeny class 441.1-c contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
441.1-c1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -8 a - 13\) , \( -19 a - 34\bigr] \)
441.1-c2	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 6 a - 21\) , \( 18 a - 53\bigr] \)
441.1-c3	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -113 a - 223\) , \( -1048 a - 1861\bigr] \)
441.1-c4	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( 111 a - 336\) , \( 1047 a - 2909\bigr] \)

Rank

Rank: \( 0 \)

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