Elliptic curve isogeny class 20449.3-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-20449.3-a
• Conductor: 20449.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 20449.3-a over \(\Q(\sqrt{-3}) \)

Isogeny class 20449.3-a contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
20449.3-a1	\( \bigl[0\) , \( -a\) , \( 1\) , \( 62563 a + 54742\) , \( 9543612 a - 14087030\bigr] \)
20449.3-a2	\( \bigl[0\) , \( -a\) , \( 1\) , \( 83 a + 72\) , \( 782 a - 1200\bigr] \)
20449.3-a3	\( \bigl[0\) , \( -a\) , \( 1\) , \( 3 a + 2\) , \( -8 a + 10\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph