Elliptic curve isogeny class 1377.2-a over number field \(\Q(\sqrt{53}) \)

• Base field: \(\Q(\sqrt{53}) \)
• Label: 2.2.53.1-1377.2-a
• Conductor: 1377.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 1377.2-a over \(\Q(\sqrt{53}) \)

Isogeny class 1377.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
1377.2-a1	\( \bigl[1\) , \( -1\) , \( 1\) , \( 9 a - 38\) , \( -9 a + 37\bigr] \)
1377.2-a2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -36 a + 142\) , \( -45 a + 181\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph