Elliptic curve isogeny class 19044.5-c over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-19044.5-c
• Conductor: 19044.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 19044.5-c over \(\Q(\sqrt{-7}) \)

Isogeny class 19044.5-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
19044.5-c1	\( \bigl[1\) , \( 1\) , \( 1\) , \( 3\) , \( 3\bigr] \)
19044.5-c2	\( \bigl[1\) , \( 1\) , \( 1\) , \( -17\) , \( 11\bigr] \)
19044.5-c3	\( \bigl[1\) , \( 1\) , \( 1\) , \( -107\) , \( -457\bigr] \)
19044.5-c4	\( \bigl[1\) , \( 1\) , \( 1\) , \( -247\) , \( 1391\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph