Elliptic curve isogeny class 23716.1-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-23716.1-a
• Conductor: 23716.1
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 23716.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 23716.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
23716.1-a1	\( \bigl[1\) , \( a\) , \( 0\) , \( -392 a + 245\) , \( 300 a - 555\bigr] \)
23716.1-a2	\( \bigl[a\) , \( -1\) , \( 1\) , \( 64 a - 172\) , \( -465 a + 860\bigr] \)
23716.1-a3	\( \bigl[1\) , \( a\) , \( 0\) , \( -232 a + 145\) , \( -740 a + 1369\bigr] \)
23716.1-a4	\( \bigl[a\) , \( -1\) , \( 1\) , \( 1024 a - 2732\) , \( -28625 a + 52956\bigr] \)