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

• Label: 42978u
• Number of curves: $2$
• Conductor: $42978$
• CM: no
• Rank: $0$

Elliptic curves in class 42978u

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
42978.x1	42978u1	$[1, 0, 0, -162, -588]$	$470366406433/129621648$	$129621648$	$[2]$	$17152$	$0.26419$	$\Gamma_0(N)$-optimal
42978.x2	42978u2	$[1, 0, 0, 418, -3720]$	$8075838390047/10764183924$	$-10764183924$	$[2]$	$34304$	$0.61077$

Rank

The elliptic curves in class 42978u have rank $0$.

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
$7$	$1 - T + 7 T^{2}$	1.7.ab
$11$	$1 + 2 T + 11 T^{2}$	1.11.c
$17$	$1 - 4 T + 17 T^{2}$	1.17.ae
$23$	$1 - 3 T + 23 T^{2}$	1.23.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 42978.2.a.u

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.