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

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-504.1-d
• Conductor: 504.1
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
504.1-d1	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -1298 a - 3435\) , \( 107823 a + 285275\bigr] \)
504.1-d2	\( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 572 a + 1515\) , \( 4015 a + 10621\bigr] \)
504.1-d3	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 149 a - 386\) , \( -535 a + 1420\bigr] \)
504.1-d4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -7\) , \( -10\bigr] \)
504.1-d5	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 1829 a - 4831\) , \( -70920 a + 187641\bigr] \)
504.1-d6	\( \bigl[a + 1\) , \( a - 1\) , \( 0\) , \( 1299 a - 3431\) , \( -111258 a + 294363\bigr] \)

Rank

Rank: \( 1 \)

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