Elliptic curve isogeny class 82308.2-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-82308.2-a
• Conductor: 82308.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 82308.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 82308.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
82308.2-a1	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -76 a - 213\) , \( -593 a - 1112\bigr] \)
82308.2-a2	\( \bigl[1\) , \( 1\) , \( a + 1\) , \( -26 a - 53\) , \( 101 a + 98\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph