Elliptic curve isogeny class 147.1-f over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-147.1-f
• Conductor: 147.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 147.1-f over \(\Q(\sqrt{21}) \)

Isogeny class 147.1-f contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
147.1-f1	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -7 a - 15\) , \( -119 a - 209\bigr] \)
147.1-f2	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -252 a - 505\) , \( -4186 a - 7314\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph