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

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

Elliptic curves in class 42978.k

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
42978.k1	42978m1	$[1, 1, 1, -58, -157]$	$21601086625/4899492$	$4899492$	$[2]$	$12288$	$-0.0035968$	$\Gamma_0(N)$-optimal
42978.k2	42978m2	$[1, 1, 1, 132, -765]$	$254237645375/437473062$	$-437473062$	$[2]$	$24576$	$0.34298$

Rank

The elliptic curves in class 42978.k have 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 $\mathbb{F}_p$
$5$	$1 + 5 T^{2}$	1.5.a
$7$	$1 - 4 T + 7 T^{2}$	1.7.ae
$11$	$1 - 4 T + 11 T^{2}$	1.11.ae
$17$	$1 + 6 T + 17 T^{2}$	1.17.g
$23$	$1 + 8 T + 23 T^{2}$	1.23.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 42978.2.a.k

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 LMFDB numbering.

$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.