Elliptic curve isogeny class 19200.1-e over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-19200.1-e
• Conductor: 19200.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 19200.1-e over \(\Q(\sqrt{-3}) \)

Isogeny class 19200.1-e contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
19200.1-e1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -216\) , \( 4080\bigr] \)
19200.1-e2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 24\) , \( -144\bigr] \)
19200.1-e3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -7256\) , \( 34800\bigr] \)
19200.1-e4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -1096\) , \( 12400\bigr] \)
19200.1-e5	\( \bigl[0\) , \( -1\) , \( 0\) , \( -296\) , \( -1680\bigr] \)
19200.1-e6	\( \bigl[0\) , \( -1\) , \( 0\) , \( -5336\) , \( 151536\bigr] \)
19200.1-e7	\( \bigl[0\) , \( -1\) , \( 0\) , \( -4616\) , \( -119184\bigr] \)
19200.1-e8	\( \bigl[0\) , \( -1\) , \( 0\) , \( -85336\) , \( 9623536\bigr] \)

Rank

Rank: \( 0 \)

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