Elliptic curve isogeny class with LMFDB label 69360.bp (Cremona label 69360q)

• Label: 69360.bp
• Number of curves: $4$
• Conductor: $69360$
• CM: no
• Rank: $0$

Elliptic curves in class 69360.bp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
69360.bp1	69360q4	$[0, -1, 0, -20835840, 36613767600]$	$40472803590982276/281883375$	$6967274919951744000$	$[2]$	$3981312$	$2.7954$
69360.bp2	69360q2	$[0, -1, 0, -1328340, 548301600]$	$41948679809104/3291890625$	$20341308697956000000$	$[2, 2]$	$1990656$	$2.4489$
69360.bp3	69360q1	$[0, -1, 0, -274935, -45397458]$	$5951163357184/1129312125$	$436141589435586000$	$[2]$	$995328$	$2.1023$	$\Gamma_0(N)$-optimal
69360.bp4	69360q3	$[0, -1, 0, 1324680, 2462720832]$	$10400706415004/112060546875$	$-2769786042750000000000$	$[4]$	$3981312$	$2.7954$

Rank

The elliptic curves in class 69360.bp have rank $0$.

L-function data

Bad L-factors:

Prime	L-Factor
$2$	$1$
$3$	$1 + T$
$5$	$1 - T$
$17$	$1$

Good L-factors:

Prime	L-Factor	Isogeny Class over $\mathbb{F}_p$
$7$	$1 + 7 T^{2}$	1.7.a
$11$	$1 + 4 T + 11 T^{2}$	1.11.e
$13$	$1 - 6 T + 13 T^{2}$	1.13.ag
$19$	$1 + 4 T + 19 T^{2}$	1.19.e
$23$	$1 + 8 T + 23 T^{2}$	1.23.i
$29$	$1 - 6 T + 29 T^{2}$	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 69360.bp do not have complex multiplication.

Modular form 69360.2.a.bp

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.