Elliptic curve isogeny class 126976.2-e over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-126976.2-e
• Conductor: 126976.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 126976.2-e over \(\Q(\sqrt{-3}) \)

Isogeny class 126976.2-e contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
126976.2-e1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 48032 a + 35167\) , \( -5257632 a + 8569025\bigr] \)
126976.2-e2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 32 a - 33\) , \( -32 a + 65\bigr] \)
126976.2-e3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -608 a - 353\) , \( -416 a - 5503\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph