Elliptic curve isogeny class with LMFDB label 504.f (Cremona label 504d)

• Label: 504.f
• Number of curves: $2$
• Conductor: $504$
• CM: no
• Rank: $0$

Elliptic curves in class 504.f

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
504.f1	504d2	$[0, 0, 0, -999, -12150]$	$21882096/7$	$35271936$	$[2]$	$192$	$0.42301$
504.f2	504d1	$[0, 0, 0, -54, -243]$	$-55296/49$	$-15431472$	$[2]$	$96$	$0.076434$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 504.f have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1$
$7$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 - 2 T + 5 T^{2}$	1.5.ac
$11$	$1 - 2 T + 11 T^{2}$	1.11.ac
$13$	$1 - 2 T + 13 T^{2}$	1.13.ac
$17$	$1 - 6 T + 17 T^{2}$	1.17.ag
$19$	$1 + 4 T + 19 T^{2}$	1.19.e
$23$	$1 - 6 T + 23 T^{2}$	1.23.ag
$29$	$1 + 29 T^{2}$	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 504.f do not have complex multiplication.

Modular form 504.2.a.f

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.