Elliptic curve isogeny class with Cremona label 303600gm (LMFDB label 303600.gm)

• Label: 303600gm
• Number of curves: $2$
• Conductor: $303600$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 303600gm have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(11\)	\(1 - T\)
\(23\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(13\)	\( 1 - 7 T + 13 T^{2}\)	1.13.ah
\(17\)	\( 1 - 3 T + 17 T^{2}\)	1.17.ad
\(19\)	\( 1 + 8 T + 19 T^{2}\)	1.19.i
\(29\)	\( 1 + 9 T + 29 T^{2}\)	1.29.j
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 303600gm do not have complex multiplication.

Modular form 303600.2.a.gm

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 303600gm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
303600.gm2	303600gm1	\([0, 1, 0, -50808, -2349612]\)	\(226646274673/94431744\)	\(6043631616000000\)	\([]\)	\(2239488\)	\(1.7253\)	\(\Gamma_0(N)\)-optimal
303600.gm1	303600gm2	\([0, 1, 0, -1922808, 1025522388]\)	\(12284337086925553/1165987944\)	\(74623228416000000\)	\([]\)	\(6718464\)	\(2.2746\)