Elliptic curve isogeny class 14700.2-i over number field \(\Q(\sqrt{-3}) \)

• Base field: \(\Q(\sqrt{-3}) \)
• Label: 2.0.3.1-14700.2-i
• Conductor: 14700.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 14700.2-i over \(\Q(\sqrt{-3}) \)

Isogeny class 14700.2-i contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
14700.2-i1	\( \bigl[a\) , \( 0\) , \( 1\) , \( 20352 a\) , \( -1443724\bigr] \)
14700.2-i2	\( \bigl[a\) , \( 0\) , \( 1\) , \( -1923 a\) , \( 20756\bigr] \)
14700.2-i3	\( \bigl[a\) , \( 0\) , \( 1\) , \( 577 a\) , \( 2756\bigr] \)
14700.2-i4	\( \bigl[a\) , \( 0\) , \( 1\) , \( 1472 a\) , \( -16652\bigr] \)
14700.2-i5	\( \bigl[a\) , \( 0\) , \( 1\) , \( 4357 a\) , \( -109132\bigr] \)
14700.2-i6	\( \bigl[a\) , \( 0\) , \( 1\) , \( 497 a\) , \( 4228\bigr] \)
14700.2-i7	\( \bigl[a\) , \( 0\) , \( 1\) , \( 21952 a\) , \( -1253644\bigr] \)
14700.2-i8	\( \bigl[a\) , \( 0\) , \( 1\) , \( 351232 a\) , \( -80149132\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 6 & 4 & 12 & 12 & 2 & 4 \\ 3 & 1 & 2 & 12 & 4 & 4 & 6 & 12 \\ 6 & 2 & 1 & 6 & 2 & 2 & 3 & 6 \\ 4 & 12 & 6 & 1 & 12 & 3 & 2 & 4 \\ 12 & 4 & 2 & 12 & 1 & 4 & 6 & 3 \\ 12 & 4 & 2 & 3 & 4 & 1 & 6 & 12 \\ 2 & 6 & 3 & 2 & 6 & 6 & 1 & 2 \\ 4 & 12 & 6 & 4 & 3 & 12 & 2 & 1 \end{array}\right)\)

Isogeny graph