Elliptic curve isogeny class 34596.3-d over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-34596.3-d
• Conductor: 34596.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 34596.3-d over \(\Q(\sqrt{-3}) \)

Isogeny class 34596.3-d contains 3 curves linked by isogenies of degrees dividing 25.

Curve label	Weierstrass Coefficients
34596.3-d1	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( -82463 a + 118366\) , \( 6646969 a + 8461763\bigr] \)
34596.3-d2	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 37 a + 16\) , \( 49 a + 23\bigr] \)
34596.3-d3	\( \bigl[a\) , \( -1\) , \( a + 1\) , \( 892 a - 1394\) , \( -11606 a + 2249\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 25 & 5 \\ 25 & 1 & 5 \\ 5 & 5 & 1 \end{array}\right)\)

Isogeny graph