Elliptic curve isogeny class 4900.2-e over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-4900.2-e
• Conductor: 4900.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 4900.2-e over \(\Q(\sqrt{-7}) \)

Isogeny class 4900.2-e contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
4900.2-e1	\( \bigl[1\) , \( a - 1\) , \( 0\) , \( 22 a + 2\) , \( -12 a + 28\bigr] \)
4900.2-e2	\( \bigl[1\) , \( -a\) , \( 1\) , \( -a + 69\) , \( -191 a + 84\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph