Elliptic curve isogeny class with Cremona label 277200ia (LMFDB label 277200.ia)

• Label: 277200ia
• Number of curves: $4$
• Conductor: $277200$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 277200ia have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1\)
\(7\)	\(1 - T\)
\(11\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 - 6 T + 23 T^{2}\)	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 277200ia do not have complex multiplication.

Modular form 277200.2.a.ia

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 277200ia

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
277200.ia3	277200ia1	\([0, 0, 0, -3288675, 2305233250]\)	\(-84309998289049/414124480\)	\(-19321391738880000000\)	\([2]\)	\(7962624\)	\(2.5488\)	\(\Gamma_0(N)\)-optimal
277200.ia2	277200ia2	\([0, 0, 0, -52680675, 147171969250]\)	\(346553430870203929/8300600\)	\(387272793600000000\)	\([2]\)	\(15925248\)	\(2.8954\)
277200.ia4	277200ia3	\([0, 0, 0, 8177325, 12239199250]\)	\(1296134247276791/2137096192000\)	\(-99708359933952000000000\)	\([2]\)	\(23887872\)	\(3.0981\)
277200.ia1	277200ia4	\([0, 0, 0, -56334675, 125586783250]\)	\(423783056881319689/99207416000000\)	\(4628621200896000000000000\)	\([2]\)	\(47775744\)	\(3.4447\)