Elliptic curve isogeny class 12348.2-c over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-12348.2-c
• Conductor: 12348.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 12348.2-c over \(\Q(\sqrt{-3}) \)

Isogeny class 12348.2-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
12348.2-c1	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 607 a - 512\) , \( 6234 a - 1701\bigr] \)
12348.2-c2	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 37 a + 28\) , \( 312 a - 315\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph