Elliptic curve isogeny class 19600.1-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-19600.1-b
• Conductor: 19600.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 19600.1-b over \(\Q(\sqrt{-7}) \)

Isogeny class 19600.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
19600.1-b1	\( \bigl[a\) , \( 1\) , \( a\) , \( 82 a - 897\) , \( 1339 a - 10455\bigr] \)
19600.1-b2	\( \bigl[a\) , \( -1\) , \( a\) , \( 161 a - 75\) , \( -763 a - 493\bigr] \)
19600.1-b3	\( \bigl[a\) , \( a\) , \( a\) , \( 68 a - 58\) , \( -515 a - 87\bigr] \)
19600.1-b4	\( \bigl[a\) , \( -1\) , \( a\) , \( 336 a + 275\) , \( -3073 a + 6367\bigr] \)

Rank

Rank: \( 1 \)

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