Elliptic curve isogeny class 121.1-c over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-121.1-c
• Conductor: 121.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 121.1-c over \(\Q(\sqrt{21}) \)

Isogeny class 121.1-c contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
121.1-c1	\( \bigl[0\) , \( -a\) , \( 1\) , \( 39102 a - 109483\) , \( -6365015 a + 17769325\bigr] \)
121.1-c2	\( \bigl[0\) , \( -a\) , \( 1\) , \( 52 a - 143\) , \( -525 a + 1465\bigr] \)
121.1-c3	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -2 a - 1\) , \( -5 a - 10\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph