Elliptic curve isogeny class 4096.1-e over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-4096.1-e
• Conductor: 4096.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 4096.1-e over \(\Q(\sqrt{3}) \)

Isogeny class 4096.1-e contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
4096.1-e1	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 10 a - 18\) , \( 16 a - 28\bigr] \)
4096.1-e2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 48 a - 83\) , \( 56 a - 97\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph