Elliptic curve isogeny class 53361.3-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-53361.3-b
• Conductor: 53361.3
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-3}) \)

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 53361.3-b over \(\Q(\sqrt{-3}) \)

Isogeny class 53361.3-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
53361.3-b1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -17 a + 56\) , \( 74 a + 88\bigr] \)
53361.3-b2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -7 a - 9\) , \( 15 a + 6\bigr] \)