Elliptic curve isogeny class 1183.3-g over number field \(\Q(\sqrt{53}) \)

• Base field: \(\Q(\sqrt{53}) \)
• Label: 2.2.53.1-1183.3-g
• Conductor: 1183.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 1183.3-g over \(\Q(\sqrt{53}) \)

Isogeny class 1183.3-g contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
1183.3-g1	\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( -112430 a - 354439\) , \( -39130752 a - 122894996\bigr] \)
1183.3-g2	\( \bigl[0\) , \( -a + 1\) , \( a + 1\) , \( -10 a - 29\) , \( -829 a - 2604\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph