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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-19600.5-c
• 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-c over \(\Q(\sqrt{-7}) \)

Isogeny class 19600.5-c contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
19600.5-c1	\( \bigl[0\) , \( 1\) , \( a + 1\) , \( 2758 a - 919\) , \( -37260 a - 55453\bigr] \)
19600.5-c2	\( \bigl[0\) , \( 1\) , \( a + 1\) , \( 28 a - 9\) , \( 50 a + 57\bigr] \)
19600.5-c3	\( \bigl[0\) , \( 1\) , \( a + 1\) , \( -182 a + 61\) , \( -167 a - 132\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph