Elliptic curve isogeny class with LMFDB label 137904.bk (Cremona label 137904bx)

• Label: 137904.bk
• Number of curves: $2$
• Conductor: $137904$
• CM: no
• Rank: $0$

Elliptic curves in class 137904.bk

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
137904.bk1	137904bx1	$[0, -1, 0, -211137, -37270728]$	$13478411517952/304317$	$23502080551248$	$[2]$	$645120$	$1.6798$	$\Gamma_0(N)$-optimal
137904.bk2	137904bx2	$[0, -1, 0, -203532, -40087620]$	$-754612278352/127035441$	$-156973007344068864$	$[2]$	$1290240$	$2.0264$

Rank

The elliptic curves in class 137904.bk have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1 + T$
$13$	$1$
$17$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 - 2 T + 5 T^{2}$	1.5.ac
$7$	$1 - 2 T + 7 T^{2}$	1.7.ac
$11$	$1 + 2 T + 11 T^{2}$	1.11.c
$19$	$1 + 6 T + 19 T^{2}$	1.19.g
$23$	$1 + 4 T + 23 T^{2}$	1.23.e
$29$	$1 + 6 T + 29 T^{2}$	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 137904.bk do not have complex multiplication.

Modular form 137904.2.a.bk

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.