Elliptic curve isogeny class with Cremona label 185130en (LMFDB label 185130.bb)

• Label: 185130en
• Number of curves: $2$
• Conductor: $185130$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 185130en have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(11\)	\(1\)
\(17\)	\(1 - T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 185130en do not have complex multiplication.

Modular form 185130.2.a.en

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 185130en

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
185130.bb1	185130en1	\([1, -1, 0, -8190, 249156]\)	\(47045881/6800\)	\(8781982189200\)	\([2]\)	\(537600\)	\(1.2090\)	\(\Gamma_0(N)\)-optimal
185130.bb2	185130en2	\([1, -1, 0, 13590, 1333800]\)	\(214921799/722500\)	\(-933085607602500\)	\([2]\)	\(1075200\)	\(1.5555\)