Elliptic curve isogeny class 77500.1-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-77500.1-b
• Conductor: 77500.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 77500.1-b over \(\Q(\sqrt{-3}) \)

Isogeny class 77500.1-b contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
77500.1-b1	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 137 a + 238\) , \( -132 a + 1492\bigr] \)
77500.1-b2	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 12 a - 12\) , \( -7 a - 8\bigr] \)
77500.1-b3	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( -13738 a - 18762\) , \( -1281257 a - 812508\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph