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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-4900.2-d
• Conductor: 4900.2
• Rank: \( 0 \)

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

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

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

Isogeny class 4900.2-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
4900.2-d1	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -5227 a - 1\) , \( -178144 a + 145184\bigr] \)
4900.2-d2	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( -327 a - 1\) , \( -2724 a + 2104\bigr] \)
4900.2-d3	\( \bigl[1\) , \( a - 1\) , \( a\) , \( -822 a + 240\) , \( -9198 a + 12688\bigr] \)
4900.2-d4	\( \bigl[1\) , \( a - 1\) , \( a\) , \( -52 a + 100\) , \( -434 a - 24\bigr] \)
4900.2-d5	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 5 a - 138\) , \( -206 a + 392\bigr] \)
4900.2-d6	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -4 a - 182\) , \( 12 a - 1004\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 2 & 8 & 4 \\ 4 & 2 & 2 & 1 & 4 & 2 \\ 4 & 2 & 8 & 4 & 1 & 8 \\ 8 & 4 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph