Elliptic curve isogeny class 7056.1-c over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-7056.1-c
• Conductor: 7056.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 7056.1-c over \(\Q(\sqrt{-7}) \)

Isogeny class 7056.1-c contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
7056.1-c1	\( \bigl[a\) , \( -a\) , \( 0\) , \( -714 a + 476\) , \( 13671 a - 33418\bigr] \)
7056.1-c2	\( \bigl[a\) , \( -a\) , \( 0\) , \( 21 a - 14\) , \( 0\bigr] \)
7056.1-c3	\( \bigl[a\) , \( -a\) , \( 0\) , \( -84 a + 56\) , \( 63 a - 154\bigr] \)
7056.1-c4	\( \bigl[a\) , \( -a\) , \( 0\) , \( -819 a + 546\) , \( -5670 a + 13860\bigr] \)
7056.1-c5	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 7 a - 79\) , \( 4 a - 287\bigr] \)
7056.1-c6	\( \bigl[a\) , \( 0\) , \( a\) , \( 20 a + 62\) , \( 168 a - 229\bigr] \)
7056.1-c7	\( \bigl[a\) , \( -a\) , \( 0\) , \( -1029 a + 686\) , \( 8568 a - 20944\bigr] \)
7056.1-c8	\( \bigl[a\) , \( -a\) , \( 0\) , \( -16464 a + 10976\) , \( 536445 a - 1311310\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 8 & 4 & 8 & 16 & 16 & 2 & 4 \\ 8 & 1 & 2 & 4 & 2 & 2 & 4 & 8 \\ 4 & 2 & 1 & 2 & 4 & 4 & 2 & 4 \\ 8 & 4 & 2 & 1 & 8 & 8 & 4 & 8 \\ 16 & 2 & 4 & 8 & 1 & 4 & 8 & 16 \\ 16 & 2 & 4 & 8 & 4 & 1 & 8 & 16 \\ 2 & 4 & 2 & 4 & 8 & 8 & 1 & 2 \\ 4 & 8 & 4 & 8 & 16 & 16 & 2 & 1 \end{array}\right)\)

Isogeny graph