Elliptic curve isogeny class with Cremona label 35568s (LMFDB label 35568.l)

• Label: 35568s
• Number of curves: $4$
• Conductor: $35568$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 35568s have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(13\)	\(1 + T\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(7\)	\( 1 + 3 T + 7 T^{2}\)	1.7.d
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(23\)	\( 1 - 3 T + 23 T^{2}\)	1.23.ad
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 35568s do not have complex multiplication.

Modular form 35568.2.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 35568s

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
35568.l3	35568s1	\([0, 0, 0, -180066, -29410045]\)	\(55356847905445888/60021\)	\(700084944\)	\([2]\)	\(92160\)	\(1.4161\)	\(\Gamma_0(N)\)-optimal
35568.l2	35568s2	\([0, 0, 0, -180111, -29394610]\)	\(3462397543530448/3602520441\)	\(672316774781184\)	\([2, 2]\)	\(184320\)	\(1.7627\)
35568.l4	35568s3	\([0, 0, 0, -136371, -44030014]\)	\(-375718260235972/904469833683\)	\(-675183112965024768\)	\([4]\)	\(368640\)	\(2.1093\)
35568.l1	35568s4	\([0, 0, 0, -224571, -13771366]\)	\(1677865892403172/861235747047\)	\(642909040227597312\)	\([2]\)	\(368640\)	\(2.1093\)