Elliptic curve isogeny class 4.1-e over number field \(\Q(\sqrt{113}) \)

• Base field: \(\Q(\sqrt{113}) \)
• Label: 2.2.113.1-4.1-e
• Conductor: 4.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{113}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 28 \); class number \(1\).

Elliptic curves in class 4.1-e over \(\Q(\sqrt{113}) \)

Isogeny class 4.1-e contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
4.1-e1	\( \bigl[1\) , \( 0\) , \( a\) , \( -2260548 a - 10884701\) , \( -5564451285 a - 26793238627\bigr] \)
4.1-e2	\( \bigl[1\) , \( a\) , \( 0\) , \( 186564 a - 1084871\) , \( 91146540 a - 530023767\bigr] \)
4.1-e3	\( \bigl[1\) , \( a\) , \( 0\) , \( -76 a - 359\) , \( 300 a + 1441\bigr] \)
4.1-e4	\( \bigl[1\) , \( a\) , \( 0\) , \( -2861 a - 13769\) , \( -197859 a - 952709\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph