Elliptic curve isogeny class 361.1-b over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-361.1-b
• Conductor: 361.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 361.1-b over \(\Q(\sqrt{21}) \)

Isogeny class 361.1-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
361.1-b1	\( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -3847 a - 6922\) , \( 199428 a + 357277\bigr] \)
361.1-b2	\( \bigl[0\) , \( a\) , \( 1\) , \( 47 a - 129\) , \( -308 a + 860\bigr] \)
361.1-b3	\( \bigl[0\) , \( a\) , \( 1\) , \( -3 a + 11\) , \( 2 a - 5\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph