Elliptic curve isogeny class 847.5-e over number field \(\Q(\sqrt{53}) \)

• Base field: \(\Q(\sqrt{53}) \)
• Label: 2.2.53.1-847.5-e
• Conductor: 847.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 847.5-e over \(\Q(\sqrt{53}) \)

Isogeny class 847.5-e contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
847.5-e1	\( \bigl[0\) , \( a - 1\) , \( a\) , \( -6 a - 17\) , \( -12 a - 111\bigr] \)
847.5-e2	\( \bigl[0\) , \( a - 1\) , \( a\) , \( 3284 a - 32777\) , \( 602541 a - 1491888\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph