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

• Label: 368082dl
• Number of curves: $2$
• Conductor: $368082$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 368082dl 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
\(17\)	\( 1 + 8 T + 17 T^{2}\)	1.17.i
\(19\)	\( 1 + 6 T + 19 T^{2}\)	1.19.g
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 368082.2.a.dl

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 368082dl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
368082.dl2	368082dl1	\([1, -1, 0, -61105446, -471521783628]\)	\(-4047806261953/13066420224\)	\(-81451741513419330152546304\)	\([2]\)	\(162570240\)	\(3.6582\)	\(\Gamma_0(N)\)-optimal
368082.dl1	368082dl2	\([1, -1, 0, -1356754086, -19212042842316]\)	\(44308125149913793/61165323648\)	\(381284395110047446758119808\)	\([2]\)	\(325140480\)	\(4.0048\)