Elliptic curve isogeny class 338.1-c over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-338.1-c
• Conductor: 338.1
• Rank: \( 1 \)

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

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 338.1-c over \(\Q(\sqrt{3}) \)

Isogeny class 338.1-c contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
338.1-c1	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 11910 a - 20632\) , \( 1024704 a - 1774842\bigr] \)
338.1-c2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph