Elliptic curve isogeny class with Cremona label 174240r (LMFDB label 174240.g)

• Label: 174240r
• Number of curves: $4$
• Conductor: $174240$
• CM: no
• Rank: $0$

Elliptic curves in class 174240r

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
174240.g3	174240r1	$[0, 0, 0, -33033, -2225432]$	$48228544/2025$	$167374248782400$	$[2, 2]$	$737280$	$1.4940$	$\Gamma_0(N)$-optimal
174240.g2	174240r2	$[0, 0, 0, -87483, 6998398]$	$111980168/32805$	$21691702642199040$	$[2]$	$1474560$	$1.8406$
174240.g4	174240r3	$[0, 0, 0, 15972, -8262848]$	$85184/5625$	$-29755422005760000$	$[2]$	$1474560$	$1.8406$
174240.g1	174240r4	$[0, 0, 0, -523083, -145614062]$	$23937672968/45$	$29755422005760$	$[2]$	$1474560$	$1.8406$

Rank

The elliptic curves in class 174240r have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1$
$5$	$1 + T$
$11$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$7$	$1 + 2 T + 7 T^{2}$	1.7.c
$13$	$1 - 6 T + 13 T^{2}$	1.13.ag
$17$	$1 + 17 T^{2}$	1.17.a
$19$	$1 + 6 T + 19 T^{2}$	1.19.g
$23$	$1 - 8 T + 23 T^{2}$	1.23.ai
$29$	$1 - 4 T + 29 T^{2}$	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 174240r do not have complex multiplication.

Modular form 174240.2.a.r

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.