Elliptic curve isogeny class 28.2-c over number field \(\Q(\sqrt{53}) \)

• Base field: \(\Q(\sqrt{53}) \)
• Label: 2.2.53.1-28.2-c
• Conductor: 28.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 28.2-c over \(\Q(\sqrt{53}) \)

Isogeny class 28.2-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
28.2-c1	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 23 a - 84\) , \( -109 a + 463\bigr] \)
28.2-c2	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 3 a - 4\) , \( -a + 11\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph