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

• Base field: \(\Q(\sqrt{53}) \)
• Label: 2.2.53.1-49.1-b
• 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-b over \(\Q(\sqrt{53}) \)

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

Curve label	Weierstrass Coefficients
49.1-b1	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -24 a - 79\) , \( -181 a - 571\bigr] \)
49.1-b2	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( a + 1\) , \( a + 2\bigr] \)
49.1-b3	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -4 a - 19\) , \( -21 a - 65\bigr] \)
49.1-b4	\( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -394 a - 1244\) , \( -9026 a - 28342\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph