Elliptic curve isogeny class with Cremona label 188272a (LMFDB label 188272.a)

• Label: 188272a
• Number of curves: $2$
• Conductor: $188272$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 188272a have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(7\)	\(1 - T\)
\(41\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T + 3 T^{2}\)	1.3.d
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + 13 T^{2}\)	1.13.a
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
\(29\)	\( 1 - 5 T + 29 T^{2}\)	1.29.af
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 188272a do not have complex multiplication.

Modular form 188272.2.a.a

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.

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 188272a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
188272.a2	188272a1	\([0, 0, 0, -520509883, -4207489621526]\)	\(801581275315909089/70810888830976\)	\(1377726887301114387534708736\)	\([]\)	\(142248960\)	\(3.9477\)	\(\Gamma_0(N)\)-optimal
188272.a1	188272a2	\([0, 0, 0, -258505866043, 50588723080889194]\)	\(98191033604529537629349729/10906239337336\)	\(212196449196608566239133696\)	\([]\)	\(995742720\)	\(4.9207\)