Elliptic curve isogeny class 432.2-k over number field \(\Q(\sqrt{7}) \)

• Base field: \(\Q(\sqrt{7}) \)
• Label: 2.2.28.1-432.2-k
• Conductor: 432.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 432.2-k over \(\Q(\sqrt{7}) \)

Isogeny class 432.2-k contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
432.2-k1	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -29 a - 78\) , \( -431 a - 1141\bigr] \)
432.2-k2	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -909 a - 2408\) , \( -4797 a - 12693\bigr] \)
432.2-k3	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -679 a - 1798\) , \( -16143 a - 42711\bigr] \)
432.2-k4	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -10849 a - 28708\) , \( -1008897 a - 2669289\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph