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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-3750.1-l
• Conductor: 3750.1
• Rank: \( 1 \)

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

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

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

Isogeny class 3750.1-l contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
3750.1-l1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -338\) , \( -7969\bigr] \)
3750.1-l2	\( \bigl[1\) , \( 1\) , \( 1\) , \( 37\) , \( 281\bigr] \)
3750.1-l3	\( \bigl[1\) , \( 1\) , \( 1\) , \( -11338\) , \( -67969\bigr] \)
3750.1-l4	\( \bigl[1\) , \( 1\) , \( 1\) , \( -1713\) , \( -24219\bigr] \)
3750.1-l5	\( \bigl[1\) , \( 1\) , \( 1\) , \( -463\) , \( 3281\bigr] \)
3750.1-l6	\( \bigl[1\) , \( 1\) , \( 1\) , \( -8338\) , \( -295969\bigr] \)
3750.1-l7	\( \bigl[1\) , \( 1\) , \( 1\) , \( -7213\) , \( 232781\bigr] \)
3750.1-l8	\( \bigl[1\) , \( 1\) , \( 1\) , \( -133338\) , \( -18795969\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph