Elliptic curve isogeny class 1600.1-c over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1600.1-c
• Conductor: 1600.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1600.1-c over \(\Q(\sqrt{21}) \)

Isogeny class 1600.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1600.1-c1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 65 a + 117\) , \( 816 a + 1462\bigr] \)
1600.1-c2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -35 a - 63\) , \( 144 a + 258\bigr] \)
1600.1-c3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 10 a - 28\) , \( 24 a - 67\bigr] \)
1600.1-c4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 535 a - 1498\) , \( -10224 a + 28542\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph