Elliptic curve isogeny class 71424.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-71424.1-a
• Conductor: 71424.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 71424.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 71424.1-a contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
71424.1-a1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -264 a - 456\) , \( 4776 a - 1812\bigr] \)
71424.1-a2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -24 a + 24\) , \( -24 a + 12\bigr] \)
71424.1-a3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 26376 a + 36024\) , \( -4499544 a + 5180172\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph