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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-4900.2-i
• 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-i over \(\Q(\sqrt{-7}) \)

Isogeny class 4900.2-i contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
4900.2-i1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -71\) , \( 265\bigr] \)
4900.2-i2	\( \bigl[1\) , \( a\) , \( a\) , \( 14 a + 52\) , \( 191 a - 186\bigr] \)
4900.2-i3	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( -15 a + 66\) , \( -192 a + 5\bigr] \)
4900.2-i4	\( \bigl[1\) , \( 0\) , \( 0\) , \( -1191\) , \( 15721\bigr] \)

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