Elliptic curve isogeny class 5000.1-f over number field \(\Q(\sqrt{3}) \)

• Base field: \(\Q(\sqrt{3}) \)
• Label: 2.2.12.1-5000.1-f
• Conductor: 5000.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 5000.1-f over \(\Q(\sqrt{3}) \)

Isogeny class 5000.1-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
5000.1-f1	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -325 a + 571\) , \( -7684 a + 13325\bigr] \)
5000.1-f2	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 175 a - 304\) , \( -1559 a + 2700\bigr] \)
5000.1-f3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -50\) , \( -125\bigr] \)
5000.1-f4	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 2675 a - 4679\) , \( -102184 a + 177075\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph