Elliptic curve isogeny class with LMFDB label 490.c (Cremona label 490a)

• Label: 490.c
• Number of curves: $2$
• Conductor: $490$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 490.c have rank $1$.

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 490.c do not have complex multiplication.

Modular form 490.2.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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 490.c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
490.c1	490a2	$[1, 0, 1, -1594, -26708]$	$-77626969/8000$	$-46118408000$	$[]$	$504$	$0.78567$
490.c2	490a1	$[1, 0, 1, 121, 46]$	$34391/20$	$-115296020$	$[3]$	$168$	$0.23636$	$\Gamma_0(N)$-optimal