Elliptic curve isogeny class 15876.2-e over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-15876.2-e
• Conductor: 15876.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 15876.2-e over \(\Q(\sqrt{-7}) \)

Isogeny class 15876.2-e contains 4 curves linked by isogenies of degrees dividing 39.

Curve label	Weierstrass Coefficients
15876.2-e1	\( \bigl[1\) , \( -1\) , \( a\) , \( -95 a - 366\) , \( 1181 a + 2614\bigr] \)
15876.2-e2	\( \bigl[1\) , \( -1\) , \( a\) , \( -17105 a + 8139\) , \( 213806 a - 2812541\bigr] \)
15876.2-e3	\( \bigl[1\) , \( -1\) , \( a\) , \( 1900 a - 996\) , \( 7285 a + 96582\bigr] \)
15876.2-e4	\( \bigl[1\) , \( -1\) , \( a\) , \( 10 a - 51\) , \( 40 a - 123\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 13 & 39 & 3 \\ 13 & 1 & 3 & 39 \\ 39 & 3 & 1 & 13 \\ 3 & 39 & 13 & 1 \end{array}\right)\)

Isogeny graph