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

• Label: 356928.gc
• Number of curves: $4$
• Conductor: $356928$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 356928.gc have rank \(0\).

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.e
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	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 356928.gc do not have complex multiplication.

Modular form 356928.2.a.gc

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 356928.gc

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
356928.gc1	356928gc4	\([0, 1, 0, -704938433, 7203036884031]\)	\(30618029936661765625/3678951124992\)	\(4655046826569632455852032\)	\([2]\)	\(111476736\)	\(3.7580\)
356928.gc2	356928gc3	\([0, 1, 0, -40403393, 131985337407]\)	\(-5764706497797625/2612665516032\)	\(-3305855366403955592527872\)	\([2]\)	\(55738368\)	\(3.4114\)
356928.gc3	356928gc2	\([0, 1, 0, -19474433, -18852792321]\)	\(645532578015625/252306960048\)	\(319248795047644845047808\)	\([2]\)	\(37158912\)	\(3.2087\)
356928.gc4	356928gc1	\([0, 1, 0, 3888127, -2120526849]\)	\(5137417856375/4510142208\)	\(-5706768711903942279168\)	\([2]\)	\(18579456\)	\(2.8621\)	\(\Gamma_0(N)\)-optimal