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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-1458.1-p
• 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-p over \(\Q(\sqrt{3}) \)

Isogeny class 1458.1-p contains 4 curves linked by isogenies of degrees dividing 21.

Curve label	Weierstrass Coefficients
1458.1-p1	\( \bigl[1\) , \( -1\) , \( a\) , \( 60322 a - 104487\) , \( 10598940 a - 18357907\bigr] \)
1458.1-p2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -5\) , \( 5\bigr] \)
1458.1-p3	\( \bigl[a\) , \( 0\) , \( a + 1\) , \( 5302 a - 9186\) , \( 563242 a - 975566\bigr] \)
1458.1-p4	\( \bigl[a\) , \( 0\) , \( 0\) , \( 3\) , \( 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 21 & 3 & 7 \\ 21 & 1 & 7 & 3 \\ 3 & 7 & 1 & 21 \\ 7 & 3 & 21 & 1 \end{array}\right)\)

Isogeny graph