Elliptic curve isogeny class 1792.1-bp over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1792.1-bp
• Conductor: 1792.1
• Rank: \( 2 \)

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

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

Elliptic curves in class 1792.1-bp over \(\Q(\sqrt{21}) \)

Isogeny class 1792.1-bp contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
1792.1-bp1	\( \bigl[0\) , \( -a\) , \( 0\) , \( 13642 a - 38195\) , \( 1328439 a - 3708446\bigr] \)
1792.1-bp2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 42 a - 115\) , \( -425 a + 1186\bigr] \)
1792.1-bp3	\( \bigl[0\) , \( -a\) , \( 0\) , \( -358 a + 1005\) , \( 9191 a - 25662\bigr] \)
1792.1-bp4	\( \bigl[0\) , \( -a\) , \( 0\) , \( 2842 a - 7955\) , \( 104295 a - 291134\bigr] \)
1792.1-bp5	\( \bigl[0\) , \( -a\) , \( 0\) , \( 842 a - 2355\) , \( -19657 a + 54882\bigr] \)
1792.1-bp6	\( \bigl[0\) , \( -a\) , \( 0\) , \( 218442 a - 611635\) , \( 84485431 a - 235853342\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph