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

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-145152.2-d
• Conductor: 145152.2
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
145152.2-d1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 48 a - 51\) , \( -240 a + 50\bigr] \)
145152.2-d2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -432 a + 429\) , \( 4464 a + 722\bigr] \)
145152.2-d3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 48 a + 1629\) , \( -29808 a + 15842\bigr] \)
145152.2-d4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -48 a - 219\) , \( 432 a + 1226\bigr] \)
145152.2-d5	\( \bigl[0\) , \( 0\) , \( 0\) , \( 4848 a - 4371\) , \( -138672 a + 53138\bigr] \)

Rank

Rank: \( 0 \)

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