Elliptic curve isogeny class 17500.2-f over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-17500.2-f
• Conductor: 17500.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 17500.2-f over \(\Q(\sqrt{-7}) \)

Isogeny class 17500.2-f contains 12 curves linked by isogenies of degrees dividing 36.

Curve label	Weierstrass Coefficients
17500.2-f1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -4263\) , \( -109219\bigr] \)
17500.2-f2	\( \bigl[1\) , \( a\) , \( a\) , \( 250 a + 153\) , \( 838 a - 3853\bigr] \)
17500.2-f3	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -251 a + 403\) , \( -839 a - 3015\bigr] \)
17500.2-f4	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -a + 28\) , \( 36 a - 15\bigr] \)
17500.2-f5	\( \bigl[1\) , \( a\) , \( a\) , \( 28\) , \( -37 a + 22\bigr] \)
17500.2-f6	\( \bigl[1\) , \( 1\) , \( 1\) , \( -13\) , \( 31\bigr] \)
17500.2-f7	\( \bigl[1\) , \( 1\) , \( 1\) , \( 112\) , \( -719\bigr] \)
17500.2-f8	\( \bigl[1\) , \( a\) , \( a\) , \( -750 a - 222\) , \( 3213 a - 19478\bigr] \)
17500.2-f9	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 749 a - 972\) , \( -3214 a - 16265\bigr] \)
17500.2-f10	\( \bigl[1\) , \( 1\) , \( 1\) , \( -888\) , \( -8719\bigr] \)
17500.2-f11	\( \bigl[1\) , \( 1\) , \( 1\) , \( -263\) , \( 1531\bigr] \)
17500.2-f12	\( \bigl[1\) , \( 1\) , \( 1\) , \( -68263\) , \( -6893219\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrrrr} 1 & 6 & 6 & 18 & 18 & 9 & 3 & 2 & 2 & 6 & 18 & 2 \\ 6 & 1 & 4 & 12 & 3 & 6 & 2 & 3 & 12 & 4 & 12 & 12 \\ 6 & 4 & 1 & 3 & 12 & 6 & 2 & 12 & 3 & 4 & 12 & 12 \\ 18 & 12 & 3 & 1 & 4 & 2 & 6 & 36 & 9 & 12 & 4 & 36 \\ 18 & 3 & 12 & 4 & 1 & 2 & 6 & 9 & 36 & 12 & 4 & 36 \\ 9 & 6 & 6 & 2 & 2 & 1 & 3 & 18 & 18 & 6 & 2 & 18 \\ 3 & 2 & 2 & 6 & 6 & 3 & 1 & 6 & 6 & 2 & 6 & 6 \\ 2 & 3 & 12 & 36 & 9 & 18 & 6 & 1 & 4 & 12 & 36 & 4 \\ 2 & 12 & 3 & 9 & 36 & 18 & 6 & 4 & 1 & 12 & 36 & 4 \\ 6 & 4 & 4 & 12 & 12 & 6 & 2 & 12 & 12 & 1 & 3 & 3 \\ 18 & 12 & 12 & 4 & 4 & 2 & 6 & 36 & 36 & 3 & 1 & 9 \\ 2 & 12 & 12 & 36 & 36 & 18 & 6 & 4 & 4 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph