Elliptic curve isogeny class 106875.2-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-106875.2-c
• Conductor: 106875.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 106875.2-c over \(\Q(\sqrt{-3}) \)

Isogeny class 106875.2-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
106875.2-c1	\( \bigl[1\) , \( a\) , \( a + 1\) , \( -625 a + 3257\) , \( -21137 a - 1137\bigr] \)
106875.2-c2	\( \bigl[1\) , \( a\) , \( a + 1\) , \( -10000 a + 42632\) , \( -3167387 a + 623238\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph