Elliptic curve isogeny class 4.1-a over number field 3.3.733.1

• Base field: 3.3.733.1
• Label: 3.3.733.1-4.1-a
• Conductor: 4.1
• Rank: \( 1 \)

Base field 3.3.733.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 7 x + 8 \); class number \(1\).

Elliptic curves in class 4.1-a over 3.3.733.1

Isogeny class 4.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
4.1-a1	\( \bigl[1\) , \( a - 1\) , \( 1\) , \( -249848597 a^{2} - 379319816 a + 793737515\) , \( 2203418510276 a^{2} + 3345227116373 a - 6999982998532\bigr] \)
4.1-a2	\( \bigl[a + 1\) , \( -a^{2} + 6\) , \( a^{2} + a - 4\) , \( -6 a^{2} - 6 a + 28\) , \( -9 a^{2} - 12 a + 33\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph