Elliptic curve isogeny class with Cremona label 221760dg (LMFDB label 221760.fr)

• Label: 221760dg
• Number of curves: $4$
• Conductor: $221760$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 221760dg have rank \(1\).

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 \(\mathbb{F}_p\)
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 221760.2.a.dg

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 221760dg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
221760.fr3	221760dg1	\([0, 0, 0, -41628, -3269072]\)	\(667932971344/3465\)	\(41385738240\)	\([2]\)	\(393216\)	\(1.2338\)	\(\Gamma_0(N)\)-optimal
221760.fr2	221760dg2	\([0, 0, 0, -42348, -3150128]\)	\(175798419556/12006225\)	\(573606332006400\)	\([2, 2]\)	\(786432\)	\(1.5803\)
221760.fr1	221760dg3	\([0, 0, 0, -133068, 14885008]\)	\(2727138195938/576489375\)	\(55084417597440000\)	\([2]\)	\(1572864\)	\(1.9269\)
221760.fr4	221760dg4	\([0, 0, 0, 36852, -13572848]\)	\(57925453822/866412855\)	\(-82787037517578240\)	\([2]\)	\(1572864\)	\(1.9269\)