Elliptic curve isogeny class 336.1-d over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-336.1-d
• Conductor: 336.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 336.1-d over \(\Q(\sqrt{21}) \)

Isogeny class 336.1-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
336.1-d1	\( \bigl[0\) , \( a\) , \( 0\) , \( 567 a - 1585\) , \( -11818 a + 32988\bigr] \)
336.1-d2	\( \bigl[0\) , \( a\) , \( 0\) , \( -33 a + 95\) , \( -34 a + 96\bigr] \)
336.1-d3	\( \bigl[0\) , \( a\) , \( 0\) , \( 142 a - 395\) , \( -531 a + 1482\bigr] \)
336.1-d4	\( \bigl[0\) , \( a\) , \( 0\) , \( 9142 a - 25595\) , \( -727659 a + 2031306\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph