Elliptic curve isogeny class 124.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-124.1-a
• Conductor: 124.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 124.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 124.1-a contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
124.1-a1	\( \bigl[a + 1\) , \( a\) , \( a\) , \( 1300 a - 550\) , \( -9800 a - 7280\bigr] \)
124.1-a2	\( \bigl[a + 1\) , \( a\) , \( a\) , \( 0\) , \( 0\bigr] \)
124.1-a3	\( \bigl[a + 1\) , \( a\) , \( a\) , \( -15 a + 5\) , \( -7 a + 21\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph