Elliptic curve isogeny class with LMFDB label 355570.l (Cremona label 355570l)

• Label: 355570.l
• Number of curves: $3$
• Conductor: $355570$
• CM: no
• Rank: $0$

Elliptic curves in class 355570.l

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
355570.l1	355570l1	$[1, 1, 0, -51433, -4511217]$	$-16954786009/370$	$-328376361970$	$[]$	$1078920$	$1.3258$	$\Gamma_0(N)$-optimal
355570.l2	355570l2	$[1, 1, 0, -17798, -10249348]$	$-702595369/50653000$	$-44954723953693000$	$[]$	$3236760$	$1.8751$
355570.l3	355570l3	$[1, 1, 0, 159987, 274668893]$	$510273943271/37000000000$	$-32837636197000000000$	$[]$	$9710280$	$2.4244$

Rank

The elliptic curves in class 355570.l have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$5$	$1 + T$
$31$	$1$
$37$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$3$	$1 - 2 T + 3 T^{2}$	1.3.ac
$7$	$1 + T + 7 T^{2}$	1.7.b
$11$	$1 + 3 T + 11 T^{2}$	1.11.d
$13$	$1 - 4 T + 13 T^{2}$	1.13.ae
$17$	$1 + 3 T + 17 T^{2}$	1.17.d
$19$	$1 - 2 T + 19 T^{2}$	1.19.ac
$23$	$1 + 6 T + 23 T^{2}$	1.23.g
$29$	$1 + 3 T + 29 T^{2}$	1.29.d
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 355570.l do not have complex multiplication.

Modular form 355570.2.a.l

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.

$\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with LMFDB labels.