Elliptic curve isogeny class with Cremona label 182070bu (LMFDB label 182070.dp)

• Label: 182070bu
• Number of curves: $2$
• Conductor: $182070$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 182070bu have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1\)
\(5\)	\(1 - T\)
\(7\)	\(1 - T\)
\(17\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 6 T + 23 T^{2}\)	1.23.ag
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 182070bu do not have complex multiplication.

Modular form 182070.2.a.bu

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 182070bu

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
182070.dp1	182070bu1	\([1, -1, 1, -13328012, -18684404081]\)	\(551105805571803/1376829440\)	\(654131351136500858880\)	\([2]\)	\(16558080\)	\(2.8715\)	\(\Gamma_0(N)\)-optimal
182070.dp2	182070bu2	\([1, -1, 1, -8334092, -32859146609]\)	\(-134745327251163/903920796800\)	\(-429452563224655075593600\)	\([2]\)	\(33116160\)	\(3.2181\)