Elliptic curve isogeny class with Cremona label 186576cv (LMFDB label 186576.dj)

• Label: 186576cv
• Number of curves: $2$
• Conductor: $186576$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 186576cv have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(13\)	\(1\)
\(23\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - 2 T + 7 T^{2}\)	1.7.ac
\(11\)	\( 1 - 6 T + 11 T^{2}\)	1.11.ag
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 2 T + 19 T^{2}\)	1.19.ac
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 186576cv do not have complex multiplication.

Modular form 186576.2.a.cv

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 186576cv

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
186576.dj2	186576cv1	\([0, 1, 0, -10872, 614628]\)	\(-28756228/16767\)	\(-82873453059072\)	\([2]\)	\(442368\)	\(1.3734\)	\(\Gamma_0(N)\)-optimal
186576.dj1	186576cv2	\([0, 1, 0, -193392, 32665140]\)	\(80919167474/14283\)	\(141191808915456\)	\([2]\)	\(884736\)	\(1.7199\)