Elliptic curve isogeny class with LMFDB label 54080.dg (Cremona label 54080bn)

• Label: 54080.dg
• Number of curves: $4$
• Conductor: $54080$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 54080.dg have rank \(0\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - 2 T + 3 T^{2}\)	1.3.ac
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(11\)	\( 1 + 6 T + 11 T^{2}\)	1.11.g
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 54080.dg do not have complex multiplication.

Modular form 54080.2.a.dg

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 54080.dg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
54080.dg1	54080bn3	\([0, -1, 0, -2244545, -1241615935]\)	\(988345570681/44994560\)	\(56932472496859381760\)	\([2]\)	\(2322432\)	\(2.5526\)
54080.dg2	54080bn1	\([0, -1, 0, -351745, 79937025]\)	\(3803721481/26000\)	\(32898294480896000\)	\([2]\)	\(774144\)	\(2.0033\)	\(\Gamma_0(N)\)-optimal
54080.dg3	54080bn2	\([0, -1, 0, -135425, 176978177]\)	\(-217081801/10562500\)	\(-13364932132864000000\)	\([2]\)	\(1548288\)	\(2.3499\)
54080.dg4	54080bn4	\([0, -1, 0, 1216575, -4728348223]\)	\(157376536199/7722894400\)	\(-9771925162156254822400\)	\([2]\)	\(4644864\)	\(2.8992\)