Elliptic curve isogeny class 6300.2-c over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-6300.2-c
• Conductor: 6300.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 6300.2-c over \(\Q(\sqrt{-7}) \)

Isogeny class 6300.2-c contains 10 curves linked by isogenies of degrees dividing 32.

Curve label	Weierstrass Coefficients
6300.2-c1	\( \bigl[1\) , \( -a + 1\) , \( a + 1\) , \( 433 a + 75\) , \( 369 a + 6433\bigr] \)
6300.2-c2	\( \bigl[1\) , \( a\) , \( a\) , \( -434 a + 509\) , \( -370 a + 6803\bigr] \)
6300.2-c3	\( \bigl[1\) , \( 0\) , \( 0\) , \( -119300\) , \( -16229850\bigr] \)
6300.2-c4	\( \bigl[1\) , \( 0\) , \( 0\) , \( 1270\) , \( -789048\bigr] \)
6300.2-c5	\( \bigl[1\) , \( 0\) , \( 0\) , \( 210\) , \( 900\bigr] \)
6300.2-c6	\( \bigl[1\) , \( 0\) , \( 0\) , \( -1070\) , \( 7812\bigr] \)
6300.2-c7	\( \bigl[1\) , \( 0\) , \( 0\) , \( -7550\) , \( -247500\bigr] \)
6300.2-c8	\( \bigl[1\) , \( 0\) , \( 0\) , \( -15070\) , \( 710612\bigr] \)
6300.2-c9	\( \bigl[1\) , \( 0\) , \( 0\) , \( -120050\) , \( -16020000\bigr] \)
6300.2-c10	\( \bigl[1\) , \( 0\) , \( 0\) , \( -1920800\) , \( -1024800150\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrr} 1 & 4 & 32 & 16 & 2 & 4 & 8 & 8 & 16 & 32 \\ 4 & 1 & 32 & 16 & 2 & 4 & 8 & 8 & 16 & 32 \\ 32 & 32 & 1 & 8 & 16 & 8 & 4 & 16 & 2 & 4 \\ 16 & 16 & 8 & 1 & 8 & 4 & 2 & 8 & 4 & 8 \\ 2 & 2 & 16 & 8 & 1 & 2 & 4 & 4 & 8 & 16 \\ 4 & 4 & 8 & 4 & 2 & 1 & 2 & 2 & 4 & 8 \\ 8 & 8 & 4 & 2 & 4 & 2 & 1 & 4 & 2 & 4 \\ 8 & 8 & 16 & 8 & 4 & 2 & 4 & 1 & 8 & 16 \\ 16 & 16 & 2 & 4 & 8 & 4 & 2 & 8 & 1 & 2 \\ 32 & 32 & 4 & 8 & 16 & 8 & 4 & 16 & 2 & 1 \end{array}\right)\)

Isogeny graph