Elliptic curve isogeny class 833.4-c over number field \(\Q(\sqrt{53}) \)

• Base field: \(\Q(\sqrt{53}) \)
• Label: 2.2.53.1-833.4-c
• Conductor: 833.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 833.4-c over \(\Q(\sqrt{53}) \)

Isogeny class 833.4-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
833.4-c1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -22 a - 69\) , \( 107 a + 336\bigr] \)
833.4-c2	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -148 a + 612\) , \( -681 a + 2820\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph