Elliptic curve isogeny class with Cremona label 92950cg (LMFDB label 92950.ce)

• Label: 92950cg
• Number of curves: $2$
• Conductor: $92950$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 92950cg have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(5\)	\(1\)
\(11\)	\(1 + T\)
\(13\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(17\)	\( 1 + 8 T + 17 T^{2}\)	1.17.i
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 5 T + 23 T^{2}\)	1.23.af
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 92950cg do not have complex multiplication.

Modular form 92950.2.a.cg

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 92950cg

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
92950.ce1	92950cg1	\([1, 1, 1, -4313, 296031]\)	\(-117649/440\)	\(-33184311875000\)	\([]\)	\(221184\)	\(1.2801\)	\(\Gamma_0(N)\)-optimal
92950.ce2	92950cg2	\([1, 1, 1, 37937, -7055469]\)	\(80062991/332750\)	\(-25095635855468750\)	\([]\)	\(663552\)	\(1.8294\)