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

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-504.1-w
• 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-w over \(\Q(\sqrt{7}) \)

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

Curve label	Weierstrass Coefficients
504.1-w1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -7\) , \( 52\bigr] \)
504.1-w2	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 18684 a + 49430\) , \( -236238 a - 625028\bigr] \)
504.1-w3	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 4709 a - 12454\) , \( 31216 a - 82586\bigr] \)
504.1-w4	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 3029 a - 8009\) , \( -148859 a + 393848\bigr] \)
504.1-w5	\( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -18681 a + 49426\) , \( 285664 a - 755804\bigr] \)
504.1-w6	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( -48386 a - 128020\) , \( 9328140 a + 24679944\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph