Elliptic curve isogeny class with Cremona label 89280do (LMFDB label 89280.fb)

• Label: 89280do
• Number of curves: $2$
• Conductor: $89280$
• CM: no
• Rank: $1$

Elliptic curves in class 89280do

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
89280.fb1	89280do1	$[0, 0, 0, -45612, -4402736]$	$-1482713947827/325058560$	$-2300728081121280$	$[]$	$387072$	$1.6684$	$\Gamma_0(N)$-optimal
89280.fb2	89280do2	$[0, 0, 0, 323028, 26448336]$	$722458663317/476656000$	$-2459440263462912000$	$[]$	$1161216$	$2.2177$

Rank

The elliptic curves in class 89280do have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1$
$5$	$1 - T$
$31$	$1 + T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$7$	$1 + 2 T + 7 T^{2}$	1.7.c
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$13$	$1 - 4 T + 13 T^{2}$	1.13.ae
$17$	$1 + 17 T^{2}$	1.17.a
$19$	$1 + 19 T^{2}$	1.19.a
$23$	$1 - 4 T + 23 T^{2}$	1.23.ae
$29$	$1 - 2 T + 29 T^{2}$	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 89280do do not have complex multiplication.

Modular form 89280.2.a.do

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.