Elliptic curve isogeny class 21.1-c over number field \(\Q(\sqrt{105}) \)

• Base field: \(\Q(\sqrt{105}) \)
• Label: 2.2.105.1-21.1-c
• Conductor: 21.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{105}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 26 \); class number \(2\).

Elliptic curves in class 21.1-c over \(\Q(\sqrt{105}) \)

Isogeny class 21.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
21.1-c1	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -22318 a - 103177\) , \( -11478705 a - 53071509\bigr] \)
21.1-c2	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 642 a + 2978\) , \( -5572 a - 25761\bigr] \)
21.1-c3	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -2638 a - 12187\) , \( -31071 a - 143655\bigr] \)
21.1-c4	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -25598 a - 118342\) , \( 5061268 a + 23400649\bigr] \)
21.1-c5	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -32158 a - 148672\) , \( -7037346 a - 32536995\bigr] \)
21.1-c6	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -514318 a - 2377927\) , \( -453535587 a - 2096910621\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph