Elliptic curve isogeny class with Cremona label 27720s (LMFDB label 27720.bh)

• Label: 27720s
• Number of curves: $4$
• Conductor: $27720$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 27720s have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(7\)	\(1 - T\)
\(11\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 2 T + 23 T^{2}\)	1.23.c
\(29\)	\( 1 + 2 T + 29 T^{2}\)	1.29.c
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 27720s do not have complex multiplication.

Modular form 27720.2.a.s

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 27720s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
27720.bh3	27720s1	\([0, 0, 0, -10407, 408634]\)	\(667932971344/3465\)	\(646652160\)	\([2]\)	\(24576\)	\(0.88718\)	\(\Gamma_0(N)\)-optimal
27720.bh2	27720s2	\([0, 0, 0, -10587, 393766]\)	\(175798419556/12006225\)	\(8962598937600\)	\([2, 2]\)	\(49152\)	\(1.2338\)
27720.bh4	27720s3	\([0, 0, 0, 9213, 1696606]\)	\(57925453822/866412855\)	\(-1293547461212160\)	\([2]\)	\(98304\)	\(1.5803\)
27720.bh1	27720s4	\([0, 0, 0, -33267, -1860626]\)	\(2727138195938/576489375\)	\(860694024960000\)	\([2]\)	\(98304\)	\(1.5803\)