Elliptic curve isogeny class with Cremona label 356928cl (LMFDB label 356928.cl)

• Label: 356928cl
• Number of curves: $4$
• Conductor: $356928$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 356928cl have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(11\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.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
\(29\)	\( 1 + 29 T^{2}\)	1.29.a
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 356928cl do not have complex multiplication.

Modular form 356928.2.a.cl

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 356928cl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
356928.cl4	356928cl1	\([0, -1, 0, 3888127, 2120526849]\)	\(5137417856375/4510142208\)	\(-5706768711903942279168\)	\([2]\)	\(18579456\)	\(2.8621\)	\(\Gamma_0(N)\)-optimal
356928.cl3	356928cl2	\([0, -1, 0, -19474433, 18852792321]\)	\(645532578015625/252306960048\)	\(319248795047644845047808\)	\([2]\)	\(37158912\)	\(3.2087\)
356928.cl2	356928cl3	\([0, -1, 0, -40403393, -131985337407]\)	\(-5764706497797625/2612665516032\)	\(-3305855366403955592527872\)	\([2]\)	\(55738368\)	\(3.4114\)
356928.cl1	356928cl4	\([0, -1, 0, -704938433, -7203036884031]\)	\(30618029936661765625/3678951124992\)	\(4655046826569632455852032\)	\([2]\)	\(111476736\)	\(3.7580\)