Elliptic curve isogeny class 504.1-r over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-504.1-r
• Conductor: 504.1
• Rank: \( 0 \)

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

Generator \(a\), with minimal polynomial \( x^{2} - 7 \); class number \(1\).

Elliptic curves in class 504.1-r over \(\Q(\sqrt{7}) \)

Isogeny class 504.1-r contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
504.1-r1	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -21 a - 35\) , \( 294 a + 735\bigr] \)
504.1-r2	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 29 a - 5\) , \( 62 a - 53\bigr] \)
504.1-r3	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -a - 5\) , \( -4 a - 11\bigr] \)
504.1-r4	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -a\) , \( -5 a - 14\bigr] \)
504.1-r5	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -31 a - 85\) , \( 114 a + 303\bigr] \)
504.1-r6	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( -521 a - 1415\) , \( 9886 a + 26287\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph