Elliptic curve isogeny class 1458.1-e over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1458.1-e
• Conductor: 1458.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 1458.1-e over \(\Q(\sqrt{3}) \)

Isogeny class 1458.1-e contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
1458.1-e1	\( \bigl[1\) , \( -1\) , \( 1\) , \( 18 a - 32\) , \( -138 a + 239\bigr] \)
1458.1-e2	\( \bigl[a\) , \( 0\) , \( 0\) , \( -18 a + 30\) , \( 108 a - 188\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph