Elliptic curve isogeny class with LMFDB label 816.g (Cremona label 816f)

• Label: 816.g
• Number of curves: $2$
• Conductor: $816$
• CM: no
• Rank: $0$

Elliptic curves in class 816.g

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
816.g1	816f2	$[0, -1, 0, -949, 11581]$	$-23100424192/14739$	$-60370944$	$[]$	$432$	$0.43392$
816.g2	816f1	$[0, -1, 0, 11, 61]$	$32768/459$	$-1880064$	$[]$	$144$	$-0.11538$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 816.g have rank $0$.

L-function data

Bad L-factors:

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

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.ae
$11$	$1 - 3 T + 11 T^{2}$	1.11.ad
$13$	$1 + T + 13 T^{2}$	1.13.b
$19$	$1 - T + 19 T^{2}$	1.19.ab
$23$	$1 + 9 T + 23 T^{2}$	1.23.j
$29$	$1 - 6 T + 29 T^{2}$	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 816.g do not have complex multiplication.

Modular form 816.2.a.g

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.

$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.