Elliptic curve isogeny class 36288.6-c over number field \(\Q(\sqrt{-7}) \)

• Base field: \(\Q(\sqrt{-7}) \)
• Label: 2.0.7.1-36288.6-c
• Conductor: 36288.6
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 36288.6-c over \(\Q(\sqrt{-7}) \)

Isogeny class 36288.6-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
36288.6-c1	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 666 a - 1342\) , \( 12573 a - 15895\bigr] \)
36288.6-c2	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -99 a - 352\) , \( 1224 a + 2375\bigr] \)
36288.6-c3	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 51 a - 49\) , \( 243 a - 141\bigr] \)
36288.6-c4	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 36 a - 82\) , \( 225 a - 271\bigr] \)