Elliptic curve isogeny class 1764.1-k over number field \(\Q(\sqrt{53}) \)

• Base field: \(\Q(\sqrt{53}) \)
• Label: 2.2.53.1-1764.1-k
• Conductor: 1764.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1764.1-k over \(\Q(\sqrt{53}) \)

Isogeny class 1764.1-k contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
1764.1-k1	\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 11 a - 37\) , \( -11 a + 53\bigr] \)
1764.1-k2	\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 131 a - 537\) , \( -1539 a + 6373\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph