Elliptic curve isogeny class 61731.3-a over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-61731.3-a
• Conductor: 61731.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 61731.3-a over \(\Q(\sqrt{-3}) \)

Isogeny class 61731.3-a contains 5 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
61731.3-a1	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 36929 a + 11540\) , \( 1351376 a - 4007862\bigr] \)
61731.3-a2	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 7731 a - 4308\) , \( -195516 a - 34450\bigr] \)
61731.3-a3	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -6699 a - 18\) , \( 251154 a - 123514\bigr] \)
61731.3-a4	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 141 a - 588\) , \( 2064 a - 5467\bigr] \)
61731.3-a5	\( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 43 a - 32\) , \( -16 a + 20\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph