Elliptic curve isogeny class 49.1-a over number field \(\Q(\sqrt{53}) \)

• Base field: \(\Q(\sqrt{53}) \)
• Label: 2.2.53.1-49.1-a
• Conductor: 49.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 49.1-a over \(\Q(\sqrt{53}) \)

Isogeny class 49.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
49.1-a1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 392 a - 1636\) , \( 9025 a - 37367\bigr] \)
49.1-a2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 22 a - 101\) , \( 180 a - 751\bigr] \)
49.1-a3	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -3 a + 4\) , \( -2 a + 4\bigr] \)
49.1-a4	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 2 a - 21\) , \( 20 a - 85\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 6 & 3 \\ 2 & 1 & 3 & 6 \\ 6 & 3 & 1 & 2 \\ 3 & 6 & 2 & 1 \end{array}\right)\)

Isogeny graph