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

• Label: 42978.t
• Number of curves: $1$
• Conductor: $42978$
• CM: no
• Rank: $2$

Elliptic curves in class 42978.t

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
42978.t1	42978t1	$[1, 0, 0, -2801, 63849]$	$-2430371866120849/367567110144$	$-367567110144$	$[]$	$129024$	$0.94860$	$\Gamma_0(N)$-optimal

Rank

The elliptic curve 42978.t1 has rank $2$.

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 $\mathbb{F}_p$
$5$	$1 + T + 5 T^{2}$	1.5.b
$7$	$1 + 5 T + 7 T^{2}$	1.7.f
$11$	$1 + 6 T + 11 T^{2}$	1.11.g
$17$	$1 + 4 T + 17 T^{2}$	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.t do not have complex multiplication.

Modular form 42978.2.a.t