Elliptic curve isogeny class 20956.2-b over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-20956.2-b
• Conductor: 20956.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 20956.2-b over \(\Q(\sqrt{-3}) \)

Isogeny class 20956.2-b contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
20956.2-b1	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -857 a - 14246\) , \( -66136 a - 659109\bigr] \)
20956.2-b2	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -7 a + 4\) , \( -6 a + 1\bigr] \)
20956.2-b3	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 23 a + 159\) , \( 529 a + 202\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph