Elliptic curve isogeny class 3750.1-j over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-3750.1-j
• Conductor: 3750.1
• Rank: \( 2 \)

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

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

Elliptic curves in class 3750.1-j over \(\Q(\sqrt{3}) \)

Isogeny class 3750.1-j contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
3750.1-j1	\( \bigl[a\) , \( -1\) , \( 0\) , \( -3\) , \( 3\bigr] \)
3750.1-j2	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 1570 a - 2717\) , \( 213729 a - 370189\bigr] \)
3750.1-j3	\( \bigl[1\) , \( a + 1\) , \( 1\) , \( 46370 a - 80317\) , \( 7122529 a - 12336589\bigr] \)
3750.1-j4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -53\) , \( 153\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph