Elliptic curve isogeny class 20000.5-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-20000.5-b
• Conductor: 20000.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 20000.5-b over \(\Q(\sqrt{-7}) \)

Isogeny class 20000.5-b contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
20000.5-b1	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -103 a + 701\) , \( -4742 a + 338\bigr] \)
20000.5-b2	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 23 a - 676\) , \( -26 a - 6422\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph