Elliptic curve isogeny class with Cremona label 53958v (LMFDB label 53958.s)

• Label: 53958v
• Number of curves: $4$
• Conductor: $53958$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 53958v have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 + T\)
\(3\)	\(1 - T\)
\(17\)	\(1 - T\)
\(23\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 5 T^{2}\)	1.5.a
\(7\)	\( 1 - T + 7 T^{2}\)	1.7.ab
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(19\)	\( 1 + T + 19 T^{2}\)	1.19.b
\(29\)	\( 1 - 4 T + 29 T^{2}\)	1.29.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 53958v do not have complex multiplication.

Modular form 53958.2.a.v

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.

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

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 53958v

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
53958.s2	53958v1	\([1, 0, 1, -135171, -19132226]\)	\(1845026709625/793152\)	\(117414961432128\)	\([2]\)	\(285120\)	\(1.6599\)	\(\Gamma_0(N)\)-optimal
53958.s3	53958v2	\([1, 0, 1, -114011, -25319410]\)	\(-1107111813625/1228691592\)	\(-181890452128545288\)	\([2]\)	\(570240\)	\(2.0064\)
53958.s1	53958v3	\([1, 0, 1, -397026, 72764596]\)	\(46753267515625/11591221248\)	\(1715916742043369472\)	\([2]\)	\(855360\)	\(2.2092\)
53958.s4	53958v4	\([1, 0, 1, 957214, 461702324]\)	\(655215969476375/1001033261568\)	\(-148188848794788413952\)	\([2]\)	\(1710720\)	\(2.5557\)