Elliptic curve isogeny class 145152.2-e over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-145152.2-e
• Conductor: 145152.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 145152.2-e over \(\Q(\sqrt{-3}) \)

Isogeny class 145152.2-e contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
145152.2-e1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 153 a - 9\) , \( 420 a - 1290\bigr] \)
145152.2-e2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -142 a - 1\) , \( 561 a - 1025\bigr] \)
145152.2-e3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -542 a + 559\) , \( 33 a + 5231\bigr] \)
145152.2-e4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 657 a - 801\) , \( -8652 a + 6270\bigr] \)
145152.2-e5	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -1615 a + 1457\) , \( -4191 a + 25936\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrr} 1 & 3 & 3 & 3 & 3 \\ 3 & 1 & 9 & 9 & 9 \\ 3 & 9 & 1 & 9 & 9 \\ 3 & 9 & 9 & 1 & 9 \\ 3 & 9 & 9 & 9 & 1 \end{array}\right)\)

Isogeny graph