Elliptic curve isogeny class 7.1-a over number field 4.4.8768.1

• Base field: 4.4.8768.1
• Label: 4.4.8768.1-7.1-a
• Conductor: 7.1
• Rank: \( 0 \)

Base field 4.4.8768.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 5 x^{2} + 6 x + 7 \); class number \(1\).

Elliptic curves in class 7.1-a over 4.4.8768.1

Isogeny class 7.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
7.1-a1	\( \bigl[a^{3} - 4 a - 3\) , \( 0\) , \( a\) , \( 31 a^{3} - 117 a^{2} + 42 a + 140\) , \( -243 a^{3} + 890 a^{2} - 260 a - 1025\bigr] \)
7.1-a2	\( \bigl[a^{2} - a - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 2\) , \( 8 a^{3} - 30 a^{2} + 8 a + 34\) , \( -29 a^{3} + 103 a^{2} - 28 a - 118\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph