Elliptic curve isogeny class 15488.5-c over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-15488.5-c
• Conductor: 15488.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 15488.5-c over \(\Q(\sqrt{-7}) \)

Isogeny class 15488.5-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
15488.5-c1	\( \bigl[a\) , \( 0\) , \( a\) , \( 146 a - 175\) , \( 566 a - 3334\bigr] \)
15488.5-c2	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( -19 a + 228\) , \( -129 a - 3075\bigr] \)
15488.5-c3	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 437 a - 316\) , \( -3079 a - 1167\bigr] \)
15488.5-c4	\( \bigl[a\) , \( -a\) , \( 0\) , \( 92 a + 527\) , \( 3344 a - 3163\bigr] \)
15488.5-c5	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 6757 a - 4956\) , \( -216039 a - 63823\bigr] \)
15488.5-c6	\( \bigl[a\) , \( -a\) , \( 0\) , \( 1372 a + 8207\) , \( 237584 a - 219739\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph