Elliptic curve isogeny class with LMFDB label 9633.p (Cremona label 9633p)

• Label: 9633.p
• Number of curves: $2$
• Conductor: $9633$
• CM: no
• Rank: $1$

Elliptic curves in class 9633.p

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
9633.p1	9633p2	$[0, 1, 1, -741966, -246241771]$	$-9358714467168256/22284891$	$-107564912442819$	$[]$	$115200$	$1.9339$
9633.p2	9633p1	$[0, 1, 1, 3324, -83131]$	$841232384/1121931$	$-5415346648179$	$[]$	$23040$	$1.1292$	$\Gamma_0(N)$-optimal

Rank

The elliptic curves in class 9633.p have rank $1$.

L-function data

Bad L-factors:

Prime	L-Factor
$3$	$1 - T$
$13$	$1$
$19$	$1 - T$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$2$	$1 - 2 T + 2 T^{2}$	1.2.ac
$5$	$1 + T + 5 T^{2}$	1.5.b
$7$	$1 + 3 T + 7 T^{2}$	1.7.d
$11$	$1 - 3 T + 11 T^{2}$	1.11.ad
$17$	$1 - 3 T + 17 T^{2}$	1.17.ad
$23$	$1 - 4 T + 23 T^{2}$	1.23.ae
$29$	$1 + 10 T + 29 T^{2}$	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 9633.p do not have complex multiplication.

Modular form 9633.2.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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.