Elliptic curve isogeny class 20000.2-d over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-20000.2-d
• Conductor: 20000.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 20000.2-d over \(\Q(\sqrt{-7}) \)

Isogeny class 20000.2-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
20000.2-d1	\( \bigl[a\) , \( -a\) , \( a\) , \( -761 a + 508\) , \( 6410 a - 15669\bigr] \)
20000.2-d2	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( 665 a - 177\) , \( 5570 a + 7886\bigr] \)
20000.2-d3	\( \bigl[a\) , \( 0\) , \( 0\) , \( 614 a - 676\) , \( -9840 a + 2484\bigr] \)
20000.2-d4	\( \bigl[a\) , \( -a\) , \( a\) , \( -12761 a + 8508\) , \( 366410 a - 895669\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph