Elliptic curve isogeny class with Cremona label 1470c (LMFDB label 1470.c)

• Label: 1470c
• Number of curves: $2$
• Conductor: $1470$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 1470c have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1 + T$
$3$	$1 + T$
$5$	$1 + T$
$7$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$11$	$1 - 6 T + 11 T^{2}$	1.11.ag
$13$	$1 + 6 T + 13 T^{2}$	1.13.g
$17$	$1 + 17 T^{2}$	1.17.a
$19$	$1 - 4 T + 19 T^{2}$	1.19.ae
$23$	$1 + 23 T^{2}$	1.23.a
$29$	$1 + 8 T + 29 T^{2}$	1.29.i
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 1470c do not have complex multiplication.

Modular form 1470.2.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 Cremona numbering.

$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 1470c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
1470.c1	1470c1	$[1, 1, 0, -1068, -8112]$	$393349474783/153600000$	$52684800000$	$[2]$	$2240$	$0.75601$	$\Gamma_0(N)$-optimal
1470.c2	1470c2	$[1, 1, 0, 3412, -53808]$	$12801408679457/11250000000$	$-3858750000000$	$[2]$	$4480$	$1.1026$