Elliptic curve isogeny class 49.2-c over number field \(\Q(\sqrt{53}) \)

• Base field: \(\Q(\sqrt{53}) \)
• Label: 2.2.53.1-49.2-c
• Conductor: 49.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 49.2-c over \(\Q(\sqrt{53}) \)

Isogeny class 49.2-c contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
49.2-c1	\( \bigl[0\) , \( a\) , \( a + 1\) , \( -4 a - 23\) , \( -25 a - 86\bigr] \)
49.2-c2	\( \bigl[0\) , \( -a\) , \( a + 1\) , \( 25 a - 98\) , \( -99 a + 401\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph