Elliptic curve isogeny class with Cremona label 165048c (LMFDB label 165048.bb)

• Label: 165048c
• Number of curves: $4$
• Conductor: $165048$
• CM: no
• Rank: $1$

Elliptic curves in class 165048c

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
165048.bb3	165048c1	$[0, 1, 0, -3879, -54918]$	$2725888/1053$	$2494108657872$	$[2]$	$202752$	$1.0777$	$\Gamma_0(N)$-optimal
165048.bb2	165048c2	$[0, 1, 0, -27684, 1725696]$	$61918288/1521$	$57641622315264$	$[2, 2]$	$405504$	$1.4243$
165048.bb1	165048c3	$[0, 1, 0, -440304, 112307856]$	$62275269892/39$	$5911961263104$	$[2]$	$811008$	$1.7709$
165048.bb4	165048c4	$[0, 1, 0, 4056, 5483712]$	$48668/85683$	$-12988578895039488$	$[2]$	$811008$	$1.7709$

Rank

The elliptic curves in class 165048c have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1 + T$
$13$	$1 - T$
$23$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$5$	$1 + 4 T + 5 T^{2}$	1.5.e
$7$	$1 - 2 T + 7 T^{2}$	1.7.ac
$11$	$1 - 2 T + 11 T^{2}$	1.11.ac
$17$	$1 + 6 T + 17 T^{2}$	1.17.g
$19$	$1 + T + 19 T^{2}$	1.19.b
$29$	$1 - 2 T + 29 T^{2}$	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 165048c do not have complex multiplication.

Modular form 165048.2.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.

$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.