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

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

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.

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	\([0, -1, 0, 1324680, 2462720832]\)	\(10400706415004/112060546875\)	\(-2769786042750000000000\)	\([4]\)	\(3981312\)	\(2.7954\)