Elliptic curve isogeny class 70189.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-70189.2-a
• Conductor: 70189.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 70189.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 70189.2-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
70189.2-a1	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 19 a + 9\) , \( -53 a + 74\bigr] \)
70189.2-a2	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 1579 a + 994\) , \( -26239 a + 47053\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph