Elliptic curve isogeny class with Cremona label 93600dn (LMFDB label 93600.et)

• Label: 93600dn
• Number of curves: $4$
• Conductor: $93600$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 93600dn have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 93600dn do not have complex multiplication.

Modular form 93600.2.a.dn

Isogeny matrix

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 93600dn

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
93600.et3	93600dn1	\([0, 0, 0, -3660825, -1525579000]\)	\(7442744143086784/2927948765625\)	\(2134474650140625000000\)	\([2, 2]\)	\(4718592\)	\(2.7912\)	\(\Gamma_0(N)\)-optimal
93600.et4	93600dn2	\([0, 0, 0, 11739300, -11012056000]\)	\(3834800837445824/3342041015625\)	\(-155926265625000000000000\)	\([2]\)	\(9437184\)	\(3.1378\)
93600.et2	93600dn3	\([0, 0, 0, -26442075, 51258577250]\)	\(350584567631475848/8259273550125\)	\(48168083344329000000000\)	\([2]\)	\(9437184\)	\(3.1378\)
93600.et1	93600dn4	\([0, 0, 0, -51192075, -140934735250]\)	\(2543984126301795848/909361981125\)	\(5303399073921000000000\)	\([2]\)	\(9437184\)	\(3.1378\)