Elliptic curve isogeny class 20449.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-20449.1-a
• Conductor: 20449.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 20449.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 20449.1-a contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
20449.1-a1	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -62563 a + 117305\) , \( -9543612 a - 4543418\bigr] \)
20449.1-a2	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -83 a + 155\) , \( -782 a - 418\bigr] \)
20449.1-a3	\( \bigl[0\) , \( a - 1\) , \( 1\) , \( -3 a + 5\) , \( 8 a + 2\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph