Elliptic curve isogeny class with Cremona label 107712en (LMFDB label 107712.dl)

• Label: 107712en
• Number of curves: $4$
• Conductor: $107712$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 107712en have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(11\)	\(1 + T\)
\(17\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(7\)	\( 1 + 2 T + 7 T^{2}\)	1.7.c
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(19\)	\( 1 + 2 T + 19 T^{2}\)	1.19.c
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 107712en do not have complex multiplication.

Modular form 107712.2.a.en

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 107712en

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
107712.dl4	107712en1	\([0, 0, 0, -3367884, -1860375152]\)	\(22106889268753393/4969545596928\)	\(949694952940637257728\)	\([2]\)	\(4128768\)	\(2.7381\)	\(\Gamma_0(N)\)-optimal
107712.dl2	107712en2	\([0, 0, 0, -50553804, -138340930160]\)	\(74768347616680342513/5615307472896\)	\(1073101969225464938496\)	\([2, 2]\)	\(8257536\)	\(3.0847\)
107712.dl3	107712en3	\([0, 0, 0, -47236044, -157282685552]\)	\(-60992553706117024753/20624795251201152\)	\(-3941459751895207721828352\)	\([2]\)	\(16515072\)	\(3.4313\)
107712.dl1	107712en4	\([0, 0, 0, -808846284, -8854154695280]\)	\(306234591284035366263793/1727485056\)	\(330127535197126656\)	\([2]\)	\(16515072\)	\(3.4313\)