Elliptic curve isogeny class with LMFDB label 42978.s (Cremona label 42978w)

• Label: 42978.s
• Number of curves: $1$
• Conductor: $42978$
• CM: no
• Rank: $1$

Elliptic curves in class 42978.s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
42978.s1	42978w1	$[1, 0, 0, -137104, 19773608]$	$-285019311441186406657/4163607870171048$	$-4163607870171048$	$[]$	$388800$	$1.8014$	$\Gamma_0(N)$-optimal

Rank

The elliptic curve 42978.s1 has rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 - T$
$3$	$1 - T$
$13$	$1 - T$
$19$	$1 + T$
$29$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 + 2 T + 5 T^{2}$	1.5.c
$7$	$1 - T + 7 T^{2}$	1.7.ab
$11$	$1 - 5 T + 11 T^{2}$	1.11.af
$17$	$1 + 4 T + 17 T^{2}$	1.17.e
$23$	$1 + 3 T + 23 T^{2}$	1.23.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 42978.s do not have complex multiplication.

Modular form 42978.2.a.s