Elliptic curve isogeny class with LMFDB label 85544.b (Cremona label 85544a)

• Label: 85544.b
• Number of curves: $1$
• Conductor: $85544$
• CM: no
• Rank: $2$

Elliptic curves in class 85544.b

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
85544.b1	85544a1	$[0, 1, 0, -2697, 47867]$	$351232/37$	$228631053568$	$[]$	$78848$	$0.91437$	$\Gamma_0(N)$-optimal

Rank

The elliptic curve 85544.b1 has rank $2$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$17$	$1$
$37$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 - T + 3 T^{2}$	1.3.ab
$5$	$1 - 2 T + 5 T^{2}$	1.5.ac
$7$	$1 + T + 7 T^{2}$	1.7.b
$11$	$1 + T + 11 T^{2}$	1.11.b
$13$	$1 + 6 T + 13 T^{2}$	1.13.g
$19$	$1 + 8 T + 19 T^{2}$	1.19.i
$23$	$1 + 6 T + 23 T^{2}$	1.23.g
$29$	$1 + 2 T + 29 T^{2}$	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 85544.b do not have complex multiplication.

Modular form 85544.2.a.b