Elliptic curve isogeny class with Cremona label 176400p (LMFDB label 176400.ea)

• Label: 176400p
• Number of curves: $2$
• Conductor: $176400$
• CM: no
• Rank: $1$

Elliptic curves in class 176400p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
176400.ea2	176400p1	$[0, 0, 0, 294000, 85750000]$	$4096/7$	$-4802902776000000000$	$[]$	$2304000$	$2.2696$	$\Gamma_0(N)$-optimal
176400.ea1	176400p2	$[0, 0, 0, -26166000, -51775850000]$	$-2887553024/16807$	$-11531769565176000000000$	$[]$	$11520000$	$3.0743$

Rank

The elliptic curves in class 176400p have rank $1$.

L-function data

Bad L-factors:

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

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 176400p do not have complex multiplication.

Modular form 176400.2.a.p

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.

$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$

Isogeny graph

The vertices are labelled with Cremona labels.