Elliptic curve isogeny class with LMFDB label 650.c (Cremona label 650e)

• Label: 650.c
• Number of curves: $2$
• Conductor: $650$
• CM: no
• Rank: $0$

Elliptic curves in class 650.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
650.c1	650e1	$[1, 0, 1, -21026, -1175052]$	$65787589563409/10400000$	$162500000000$	$[2]$	$1920$	$1.1617$	$\Gamma_0(N)$-optimal
650.c2	650e2	$[1, 0, 1, -19026, -1407052]$	$-48743122863889/26406250000$	$-412597656250000$	$[2]$	$3840$	$1.5082$

Rank

The elliptic curves in class 650.c have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$5$	$1$
$13$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 + 2 T + 3 T^{2}$	1.3.c
$7$	$1 - 4 T + 7 T^{2}$	1.7.ae
$11$	$1 + 2 T + 11 T^{2}$	1.11.c
$17$	$1 + 2 T + 17 T^{2}$	1.17.c
$19$	$1 - 6 T + 19 T^{2}$	1.19.ag
$23$	$1 + 6 T + 23 T^{2}$	1.23.g
$29$	$1 - 2 T + 29 T^{2}$	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 650.c do not have complex multiplication.

Modular form 650.2.a.c

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.