Elliptic curve isogeny class with LMFDB label 406.a (Cremona label 406a)

• Label: 406.a
• Number of curves: $2$
• Conductor: $406$
• CM: no
• Rank: $1$

Elliptic curves in class 406.a

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
406.a1	406a2	$[1, -1, 0, -4942, 134964]$	$13350003080765625/109178272$	$109178272$	$[2]$	$240$	$0.71309$
406.a2	406a1	$[1, -1, 0, -302, 2260]$	$-3051779837625/295386112$	$-295386112$	$[2]$	$120$	$0.36651$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 406.a have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$7$	$1 + T$
$29$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 + 3 T^{2}$	1.3.a
$5$	$1 + 5 T^{2}$	1.5.a
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$13$	$1 + 13 T^{2}$	1.13.a
$17$	$1 + 4 T + 17 T^{2}$	1.17.e
$19$	$1 - 4 T + 19 T^{2}$	1.19.ae
$23$	$1 + 23 T^{2}$	1.23.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 406.a do not have complex multiplication.

Modular form 406.2.a.a

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.