Elliptic curve isogeny class 20956.5-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-20956.5-b
• Conductor: 20956.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 20956.5-b over \(\Q(\sqrt{-3}) \)

Isogeny class 20956.5-b contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
20956.5-b1	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 180 a - 159\) , \( -507 a + 550\bigr] \)
20956.5-b2	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -5 a - 4\) , \( -2 a - 1\bigr] \)
20956.5-b3	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -15105 a + 14246\) , \( 65278 a - 710141\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph