Elliptic curve isogeny class with Cremona label 137904bl (LMFDB label 137904.s)

• Label: 137904bl
• Number of curves: $2$
• Conductor: $137904$
• CM: no
• Rank: $1$

Elliptic curves in class 137904bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
137904.s2	137904bl1	$[0, -1, 0, -49573, -4020992]$	$174456832000/9771957$	$754677919923408$	$[2]$	$645120$	$1.6097$	$\Gamma_0(N)$-optimal
137904.s1	137904bl2	$[0, -1, 0, -782188, -266004116]$	$42830942866000/146523$	$181053064987392$	$[2]$	$1290240$	$1.9563$

Rank

The elliptic curves in class 137904bl have rank $1$.

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 $\mathbb{F}_p$
$5$	$1 - 3 T + 5 T^{2}$	1.5.ad
$7$	$1 + 4 T + 7 T^{2}$	1.7.e
$11$	$1 - T + 11 T^{2}$	1.11.ab
$19$	$1 + 7 T + 19 T^{2}$	1.19.h
$23$	$1 + T + 23 T^{2}$	1.23.b
$29$	$1 - 2 T + 29 T^{2}$	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 137904.2.a.bl

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.