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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-17500.2-d
• 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-d over \(\Q(\sqrt{-7}) \)

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

Curve label	Weierstrass Coefficients
17500.2-d1	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 87 a + 2991\) , \( -55657 a + 43491\bigr] \)
17500.2-d2	\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 837 a + 1749\) , \( -41832 a + 53336\bigr] \)
17500.2-d3	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -38 a - 259\) , \( 468 a - 1259\bigr] \)
17500.2-d4	\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -47288 a + 36749\) , \( -2146207 a + 6589586\bigr] \)
17500.2-d5	\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 712 a - 501\) , \( -7207 a - 2414\bigr] \)
17500.2-d6	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 15712 a + 246741\) , \( -37365032 a + 24812241\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph