Elliptic curve isogeny class 15876.2-i over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-15876.2-i
• Conductor: 15876.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-7}) \)

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

Elliptic curves in class 15876.2-i over \(\Q(\sqrt{-7}) \)

Isogeny class 15876.2-i contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
15876.2-i1	\( \bigl[1\) , \( -1\) , \( 1\) , \( 22\) , \( -871\bigr] \)
15876.2-i2	\( \bigl[1\) , \( -1\) , \( 1\) , \( -126 a + 22\) , \( 252 a - 381\bigr] \)
15876.2-i3	\( \bigl[1\) , \( -1\) , \( 1\) , \( 126 a - 104\) , \( -252 a - 129\bigr] \)
15876.2-i4	\( \bigl[1\) , \( -1\) , \( 1\) , \( -1238\) , \( -15991\bigr] \)
15876.2-i5	\( \bigl[1\) , \( -1\) , \( 1\) , \( 126 a + 253\) , \( 1414 a - 2509\bigr] \)
15876.2-i6	\( \bigl[1\) , \( -1\) , \( 1\) , \( -126 a + 379\) , \( -1414 a - 1095\bigr] \)
15876.2-i7	\( \bigl[1\) , \( -1\) , \( 1\) , \( 2016 a + 4033\) , \( 92890 a - 158245\bigr] \)
15876.2-i8	\( \bigl[1\) , \( -1\) , \( 1\) , \( -2016 a + 6049\) , \( -92890 a - 65355\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 4 & 2 & 2 & 2 & 4 & 4 \\ 4 & 1 & 16 & 8 & 8 & 2 & 16 & 4 \\ 4 & 16 & 1 & 8 & 2 & 8 & 4 & 16 \\ 2 & 8 & 8 & 1 & 4 & 4 & 8 & 8 \\ 2 & 8 & 2 & 4 & 1 & 4 & 2 & 8 \\ 2 & 2 & 8 & 4 & 4 & 1 & 8 & 2 \\ 4 & 16 & 4 & 8 & 2 & 8 & 1 & 16 \\ 4 & 4 & 16 & 8 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph