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

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-15876.2-f
• 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-f over \(\Q(\sqrt{-7}) \)

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

Curve label	Weierstrass Coefficients
15876.2-f1	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -11 a - 41\) , \( -41 a - 83\bigr] \)
15876.2-f2	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( -1901 a + 904\) , \( -7286 a + 103867\bigr] \)
15876.2-f3	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 17104 a - 8966\) , \( -213807 a - 2598735\bigr] \)
15876.2-f4	\( \bigl[1\) , \( -1\) , \( a + 1\) , \( 94 a - 461\) , \( -1182 a + 3795\bigr] \)

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