Elliptic curve isogeny class 4356.5-b over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-4356.5-b
• Conductor: 4356.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 4356.5-b over \(\Q(\sqrt{-7}) \)

Isogeny class 4356.5-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
4356.5-b1	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -79 a + 79\) , \( -325 a - 685\bigr] \)
4356.5-b2	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( 41 a - 1\) , \( -13 a - 125\bigr] \)
4356.5-b3	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -424 a + 614\) , \( -1060 a - 6260\bigr] \)
4356.5-b4	\( \bigl[1\) , \( -a + 1\) , \( 0\) , \( -6694 a + 9754\) , \( -54874 a - 409456\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 6 & 3 \\ 2 & 1 & 3 & 6 \\ 6 & 3 & 1 & 2 \\ 3 & 6 & 2 & 1 \end{array}\right)\)

Isogeny graph