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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-17500.2-e
• Conductor: 17500.2
• Rank: \( 0 \)

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

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

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

Isogeny class 17500.2-e contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
17500.2-e1	\( \bigl[1\) , \( 0\) , \( a\) , \( -713 a + 212\) , \( 7206 a - 9620\bigr] \)
17500.2-e2	\( \bigl[1\) , \( 0\) , \( a\) , \( -838 a + 2587\) , \( 41831 a + 11505\bigr] \)
17500.2-e3	\( \bigl[1\) , \( a\) , \( 0\) , \( -87 a + 3078\) , \( 55657 a - 12166\bigr] \)
17500.2-e4	\( \bigl[1\) , \( a\) , \( 0\) , \( 38 a - 297\) , \( -468 a - 791\bigr] \)
17500.2-e5	\( \bigl[1\) , \( 0\) , \( a\) , \( 47287 a - 10538\) , \( 2146206 a + 4443380\bigr] \)
17500.2-e6	\( \bigl[1\) , \( a\) , \( 0\) , \( -15712 a + 262453\) , \( 37365032 a - 12552791\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 3 & 6 & 2 & 9 & 18 \\ 3 & 1 & 2 & 6 & 3 & 6 \\ 6 & 2 & 1 & 3 & 6 & 3 \\ 2 & 6 & 3 & 1 & 18 & 9 \\ 9 & 3 & 6 & 18 & 1 & 2 \\ 18 & 6 & 3 & 9 & 2 & 1 \end{array}\right)\)

Isogeny graph