Elliptic curve isogeny class with Cremona label 277248m (LMFDB label 277248.m)

• Label: 277248m
• Number of curves: $2$
• Conductor: $277248$
• CM: no
• Rank: $0$

Elliptic curves in class 277248m

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
277248.m2	277248m1	$[0, 1, 0, -1203, 68697]$	$-8000/81$	$-1951086776832$	$[2]$	$442368$	$1.0405$	$\Gamma_0(N)$-optimal
277248.m1	277248m2	$[0, 1, 0, -33693, 2362491]$	$2744000/9$	$13874394857472$	$[2]$	$884736$	$1.3871$

Rank

The elliptic curves in class 277248m have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1 - T$
$19$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 + 5 T^{2}$	1.5.a
$7$	$1 - 4 T + 7 T^{2}$	1.7.ae
$11$	$1 - 4 T + 11 T^{2}$	1.11.ae
$13$	$1 - 4 T + 13 T^{2}$	1.13.ae
$17$	$1 + 2 T + 17 T^{2}$	1.17.c
$23$	$1 - 8 T + 23 T^{2}$	1.23.ai
$29$	$1 + 8 T + 29 T^{2}$	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 277248m do not have complex multiplication.

Modular form 277248.2.a.m

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.