Elliptic curve isogeny class with Cremona label 316050ic (LMFDB label 316050.ic)

• Label: 316050ic
• Number of curves: $2$
• Conductor: $316050$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 316050ic have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1\)
\(43\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + 2 T + 13 T^{2}\)	1.13.c
\(17\)	\( 1 + 4 T + 17 T^{2}\)	1.17.e
\(19\)	\( 1 - 6 T + 19 T^{2}\)	1.19.ag
\(23\)	\( 1 + 6 T + 23 T^{2}\)	1.23.g
\(29\)	\( 1 + 10 T + 29 T^{2}\)	1.29.k
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 316050ic do not have complex multiplication.

Modular form 316050.2.a.ic

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 316050ic

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
316050.ic2	316050ic1	\([1, 0, 0, -45963, -2549583]\)	\(5841725401/1857600\)	\(3414762225000000\)	\([2]\)	\(2488320\)	\(1.6844\)	\(\Gamma_0(N)\)-optimal
316050.ic1	316050ic2	\([1, 0, 0, -290963, 58455417]\)	\(1481933914201/53916840\)	\(99113473580625000\)	\([2]\)	\(4976640\)	\(2.0310\)