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

• Base field: \(\Q(\sqrt{53}) \)
• Label: 2.2.53.1-1764.1-f
• 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-f over \(\Q(\sqrt{53}) \)

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

Curve label	Weierstrass Coefficients
1764.1-f1	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 7 a - 11\) , \( -5 a + 42\bigr] \)
1764.1-f2	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 7 a - 21\) , \( -a + 8\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph