Elliptic curve isogeny class 19600.4-d over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-19600.4-d
• Conductor: 19600.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 19600.4-d over \(\Q(\sqrt{-7}) \)

Isogeny class 19600.4-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
19600.4-d1	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 5 a - 7\) , \( -a - 9\bigr] \)
19600.4-d2	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -3 a - 6\) , \( -9 a + 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph