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

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-3750.1-e
• Conductor: 3750.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
3750.1-e1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -3\) , \( -3\bigr] \)
3750.1-e2	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 1568 a - 2716\) , \( -212160 a + 367472\bigr] \)
3750.1-e3	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 46368 a - 80316\) , \( -7076160 a + 12256272\bigr] \)
3750.1-e4	\( \bigl[1\) , \( 0\) , \( 0\) , \( -53\) , \( -153\bigr] \)

Rank

Rank: \( 0 \)

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