Elliptic curve isogeny class with LMFDB label 368082.dm (Cremona label 368082dm)

• Label: 368082.dm
• Number of curves: $4$
• Conductor: $368082$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 368082.dm have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(11\)	\(1\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 368082.dm do not have complex multiplication.

Modular form 368082.2.a.dm

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 368082.dm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
368082.dm1	368082dm4	\([1, -1, 0, -2441675781, -46135990133843]\)	\(258252149810350513/1938176193096\)	\(12081949270049628469147921416\)	\([2]\)	\(371589120\)	\(4.2186\)
368082.dm2	368082dm2	\([1, -1, 0, -255268701, 371074864837]\)	\(295102348042033/161237583936\)	\(1005101763440983062312085056\)	\([2, 2]\)	\(185794560\)	\(3.8720\)
368082.dm3	368082dm1	\([1, -1, 0, -196375581, 1057851094405]\)	\(134351465835313/205590528\)	\(1281583345490863586316288\)	\([2]\)	\(92897280\)	\(3.5254\)	\(\Gamma_0(N)\)-optimal
368082.dm4	368082dm3	\([1, -1, 0, 988848459, 2923754453725]\)	\(17154149157653327/10519679024712\)	\(-65576199298347392709679519752\)	\([2]\)	\(371589120\)	\(4.2186\)