Elliptic curve isogeny class with Cremona label 115600dg (LMFDB label 115600.co)

• Label: 115600dg
• Number of curves: $2$
• Conductor: $115600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 115600dg have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 3 T + 3 T^{2}\)	1.3.ad
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 + 3 T + 13 T^{2}\)	1.13.d
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 115600dg do not have complex multiplication.

Modular form 115600.2.a.dg

Isogeny matrix

The \((i,j)\)-th 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.

\(\left(\begin{array}{rr} 1 & 17 \\ 17 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels, and the \( \Gamma_0(N) \)-optimal curve is highlighted in blue.

Elliptic curves in class 115600dg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
115600.co2	115600dg1	\([0, -1, 0, -48648, -4113808]\)	\(-297756989/2\)	\(-85525504000\)	\([]\)	\(293760\)	\(1.2795\)	\(\Gamma_0(N)\)-optimal
115600.co1	115600dg2	\([0, -1, 0, -3054248, 2304186992]\)	\(-882216989/131072\)	\(-468135157405057024000\)	\([]\)	\(4993920\)	\(2.6961\)