Elliptic curve isogeny class 12348.3-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-12348.3-c
• Conductor: 12348.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 12348.3-c over \(\Q(\sqrt{-3}) \)

Isogeny class 12348.3-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
12348.3-c1	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 97 a + 511\) , \( -5627 a + 4437\bigr] \)
12348.3-c2	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( 67 a - 29\) , \( -275 a - 69\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph