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

• Base field: \(\Q(\sqrt{53}) \)
• Label: 2.2.53.1-1764.1-j
• Conductor: 1764.1
• Rank: \( 0 \)

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

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

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

Isogeny class 1764.1-j contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
1764.1-j1	\( \bigl[a\) , \( 1\) , \( 0\) , \( -7651 a - 24042\) , \( 591532 a + 1857453\bigr] \)
1764.1-j2	\( \bigl[a\) , \( 1\) , \( 0\) , \( -76706 a - 241072\) , \( -21970160 a - 68988956\bigr] \)
1764.1-j3	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 7371 a - 30533\) , \( -644684 a + 2669041\bigr] \)
1764.1-j4	\( \bigl[a + 1\) , \( -a + 1\) , \( 0\) , \( 1223586 a - 5069138\) , \( 1408580848 a - 5831683340\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 10 & 2 & 5 \\ 10 & 1 & 5 & 2 \\ 2 & 5 & 1 & 10 \\ 5 & 2 & 10 & 1 \end{array}\right)\)

Isogeny graph