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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-53361.3-e
• 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

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

Isogeny graph

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

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

Curve label	Weierstrass Coefficients
53361.3-e1	\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 7 a + 181\) , \( -1119 a + 741\bigr] \)
53361.3-e2	\( \bigl[a + 1\) , \( a + 1\) , \( a\) , \( 37 a - 14\) , \( -45 a - 66\bigr] \)