Elliptic curve isogeny class 18396.3-e over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-18396.3-e
• Conductor: 18396.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 18396.3-e over \(\Q(\sqrt{-3}) \)

Isogeny class 18396.3-e contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
18396.3-e1	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -53 a + 294\) , \( 1854 a - 475\bigr] \)
18396.3-e2	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 2 a + 4\) , \( -2 a + 7\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph