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

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

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

Curve label	Weierstrass Coefficients
4900.2-c1	\( \bigl[1\) , \( a - 1\) , \( a\) , \( 5226 a - 5227\) , \( 178143 a - 32959\bigr] \)
4900.2-c2	\( \bigl[1\) , \( a - 1\) , \( a\) , \( 326 a - 327\) , \( 2723 a - 619\bigr] \)
4900.2-c3	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 821 a - 582\) , \( 9197 a + 3490\bigr] \)
4900.2-c4	\( \bigl[1\) , \( -a\) , \( a + 1\) , \( 51 a + 48\) , \( 433 a - 458\bigr] \)
4900.2-c5	\( \bigl[1\) , \( a + 1\) , \( a\) , \( -4 a - 133\) , \( 201 a + 53\bigr] \)
4900.2-c6	\( \bigl[1\) , \( -a - 1\) , \( a\) , \( 5 a - 187\) , \( -17 a - 805\bigr] \)

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