Elliptic curve isogeny class 588.1-l over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-588.1-l
• Conductor: 588.1
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 588.1-l over \(\Q(\sqrt{21}) \)

Isogeny class 588.1-l contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
588.1-l1	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( 3557 a - 9962\) , \( -174085 a + 485955\bigr] \)
588.1-l2	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -118 a + 328\) , \( -1360 a + 3795\bigr] \)