Elliptic curve isogeny class 19600.5-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-19600.5-b
• Conductor: 19600.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 19600.5-b over \(\Q(\sqrt{-7}) \)

Isogeny class 19600.5-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
19600.5-b1	\( \bigl[a + 1\) , \( -a + 1\) , \( a + 1\) , \( -84 a - 815\) , \( -1340 a - 9116\bigr] \)
19600.5-b2	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -338 a + 611\) , \( 3072 a + 3294\bigr] \)
19600.5-b3	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -163 a + 86\) , \( 762 a - 1256\bigr] \)
19600.5-b4	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -68 a + 9\) , \( 456 a - 466\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph