Elliptic curve isogeny class with LMFDB label 221760.dd (Cremona label 221760fa)

• Label: 221760.dd
• Number of curves: $4$
• Conductor: $221760$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 221760.dd 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 \(\mathbb{F}_p\)
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 221760.dd do not have complex multiplication.

Modular form 221760.2.a.dd

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 221760.dd

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
221760.dd1	221760fa4	\([0, 0, 0, -15042828, -21820184048]\)	\(1969902499564819009/63690429687500\)	\(12171430656000000000000\)	\([2]\)	\(15925248\)	\(3.0117\)
221760.dd2	221760fa2	\([0, 0, 0, -2059788, 1127734288]\)	\(5057359576472449/51765560000\)	\(9892552570306560000\)	\([2]\)	\(5308416\)	\(2.4624\)
221760.dd3	221760fa1	\([0, 0, 0, -32268, 43416592]\)	\(-19443408769/4249907200\)	\(-812169913643827200\)	\([2]\)	\(2654208\)	\(2.1158\)	\(\Gamma_0(N)\)-optimal
221760.dd4	221760fa3	\([0, 0, 0, 290292, -1169538032]\)	\(14156681599871/3100231750000\)	\(-592463513714688000000\)	\([2]\)	\(7962624\)	\(2.6651\)