Elliptic curve isogeny class with Cremona label 312050j (LMFDB label 312050.j)

• Label: 312050j
• Number of curves: $2$
• Conductor: $312050$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 312050j have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(5\)	\(1\)
\(79\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 - T + 3 T^{2}\)	1.3.ab
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(11\)	\( 1 + 11 T^{2}\)	1.11.a
\(13\)	\( 1 - 4 T + 13 T^{2}\)	1.13.ae
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 8 T + 19 T^{2}\)	1.19.ai
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 6 T + 29 T^{2}\)	1.29.g
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 312050j do not have complex multiplication.

Modular form 312050.2.a.j

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 312050j

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
312050.j1	312050j1	\([1, 0, 1, -5932201, -5865675452]\)	\(-9725425/632\)	\(-1500305389543671875000\)	\([]\)	\(21715200\)	\(2.8162\)	\(\Gamma_0(N)\)-optimal
312050.j2	312050j2	\([1, 0, 1, 33074049, -7659962952]\)	\(1685478575/986078\)	\(-2340851484035514042968750\)	\([]\)	\(65145600\)	\(3.3655\)