Elliptic curve isogeny class 20956.1-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-20956.1-c
• Conductor: 20956.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 20956.1-c over \(\Q(\sqrt{-3}) \)

Isogeny class 20956.1-c contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
20956.1-c1	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -186 a + 149\) , \( 284 a + 375\bigr] \)
20956.1-c2	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 4 a + 4\) , \( -a + 1\bigr] \)
20956.1-c3	\( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 15654 a - 13496\) , \( -770131 a + 246841\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph