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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-19600.5-a
• Conductor: 19600.5
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
19600.5-a1	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -2 a + 51\) , \( 174 a + 676\bigr] \)
19600.5-a2	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -14 a + 202\) , \( 721 a - 139\bigr] \)
19600.5-a3	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -201 a + 128\) , \( -790 a + 1928\bigr] \)
19600.5-a4	\( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -3176 a + 2053\) , \( -47900 a + 113578\bigr] \)

Rank

Rank: \( 0 \)

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