Elliptic curve isogeny class 847.6-b over number field \(\Q(\sqrt{53}) \)

• Base field: \(\Q(\sqrt{53}) \)
• Label: 2.2.53.1-847.6-b
• Conductor: 847.6
• Rank: \( 2 \)

Base field \(\Q(\sqrt{53}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 13 \); class number \(1\).

Elliptic curves in class 847.6-b over \(\Q(\sqrt{53}) \)

Isogeny class 847.6-b contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
847.6-b1	\( \bigl[0\) , \( -a + 1\) , \( a\) , \( -36 a - 108\) , \( 246 a + 777\bigr] \)
847.6-b2	\( \bigl[0\) , \( -a + 1\) , \( a\) , \( -14176 a - 51978\) , \( -1963331 a - 5926760\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph