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

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-441.1-d
• Conductor: 441.1
• Rank: \( 1 \)

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

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

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

Isogeny class 441.1-d contains 6 curves linked by isogenies of degrees dividing 147.

Curve label	Weierstrass Coefficients
441.1-d1	\( \bigl[0\) , \( 0\) , \( 1\) , \( 2310 a - 7770\) , \( -113190 a + 297393\bigr] \)
441.1-d2	\( \bigl[0\) , \( 0\) , \( 1\) , \( -6510 a - 12180\) , \( 446292 a + 794890\bigr] \)
441.1-d3	\( \bigl[0\) , \( 0\) , \( 1\) , \( -2310 a - 5460\) , \( 113190 a + 184203\bigr] \)
441.1-d4	\( \bigl[0\) , \( 0\) , \( 1\) , \( 6510 a - 18690\) , \( -446292 a + 1241182\bigr] \)
441.1-d5	\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( -294 a - 527\bigr] \)
441.1-d6	\( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 12\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 147 & 49 & 3 & 21 & 7 \\ 147 & 1 & 3 & 49 & 7 & 21 \\ 49 & 3 & 1 & 147 & 21 & 7 \\ 3 & 49 & 147 & 1 & 7 & 21 \\ 21 & 7 & 21 & 7 & 1 & 3 \\ 7 & 21 & 7 & 21 & 3 & 1 \end{array}\right)\)

Isogeny graph