Elliptic curve isogeny class 126976.1-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-126976.1-c
• Conductor: 126976.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 126976.1-c over \(\Q(\sqrt{-3}) \)

Isogeny class 126976.1-c contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
126976.1-c1	\( \bigl[0\) , \( a\) , \( 0\) , \( -961 a + 353\) , \( 416 a - 5919\bigr] \)
126976.1-c2	\( \bigl[0\) , \( a\) , \( 0\) , \( -a + 33\) , \( 32 a + 33\bigr] \)
126976.1-c3	\( \bigl[0\) , \( a\) , \( 0\) , \( 83199 a - 35167\) , \( 5257632 a + 3311393\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph