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

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

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

Curve label	Weierstrass Coefficients
1764.1-i1	\( \bigl[a\) , \( -a\) , \( 1\) , \( -4 a + 14\) , \( -51 a + 211\bigr] \)
1764.1-i2	\( \bigl[a\) , \( -a\) , \( 1\) , \( 86 a - 366\) , \( -679 a + 2819\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph