Elliptic curve isogeny class 12544.5-i over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-12544.5-i
• Conductor: 12544.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 12544.5-i over \(\Q(\sqrt{-7}) \)

Isogeny class 12544.5-i contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
12544.5-i1	\( \bigl[0\) , \( a\) , \( 0\) , \( -1493 a - 297\) , \( -31268 a + 18636\bigr] \)
12544.5-i2	\( \bigl[0\) , \( -a\) , \( 0\) , \( 278 a - 178\) , \( 1637 a + 957\bigr] \)
12544.5-i3	\( \bigl[0\) , \( a\) , \( 0\) , \( -93 a - 17\) , \( -524 a + 324\bigr] \)
12544.5-i4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 9 a + 86\) , \( 260 a - 332\bigr] \)
12544.5-i5	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 37 a + 2\) , \( 20 a + 360\bigr] \)
12544.5-i6	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 149 a - 334\) , \( 1884 a - 1396\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph