Elliptic curve isogeny class with LMFDB label 2850.x (Cremona label 2850ba)

• Label: 2850.x
• Number of curves: $2$
• Conductor: $2850$
• CM: no
• Rank: $0$

Elliptic curves in class 2850.x

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
2850.x1	2850ba1	$[1, 0, 0, -2388, -45108]$	$96386901625/18468$	$288562500$	$[2]$	$2880$	$0.62403$	$\Gamma_0(N)$-optimal
2850.x2	2850ba2	$[1, 0, 0, -2138, -54858]$	$-69173457625/42633378$	$-666146531250$	$[2]$	$5760$	$0.97060$

Rank

The elliptic curves in class 2850.x have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 - T$
$3$	$1 - T$
$5$	$1$
$19$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$7$	$1 + 4 T + 7 T^{2}$	1.7.e
$11$	$1 - 4 T + 11 T^{2}$	1.11.ae
$13$	$1 + 13 T^{2}$	1.13.a
$17$	$1 - 2 T + 17 T^{2}$	1.17.ac
$23$	$1 - 2 T + 23 T^{2}$	1.23.ac
$29$	$1 + 6 T + 29 T^{2}$	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 2850.x do not have complex multiplication.

Modular form 2850.2.a.x

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.