Elliptic curve isogeny class with Cremona label 31920z (LMFDB label 31920.k)

• Label: 31920z
• Number of curves: $4$
• Conductor: $31920$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 31920z have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1 - T\)
\(7\)	\(1 - T\)
\(19\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(23\)	\( 1 + 8 T + 23 T^{2}\)	1.23.i
\(29\)	\( 1 - 6 T + 29 T^{2}\)	1.29.ag
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 31920z do not have complex multiplication.

Modular form 31920.2.a.z

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 31920z

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
31920.k4	31920z1	\([0, -1, 0, 55384, -51851664]\)	\(4586790226340951/286015269335040\)	\(-1171518543196323840\)	\([2]\)	\(387072\)	\(2.1467\)	\(\Gamma_0(N)\)-optimal
31920.k3	31920z2	\([0, -1, 0, -1792936, -888770960]\)	\(155617476551393929129/6633105589454400\)	\(27169200494405222400\)	\([2, 2]\)	\(774144\)	\(2.4933\)
31920.k2	31920z3	\([0, -1, 0, -4772136, 2834037360]\)	\(2934284984699764805929/851931751022747640\)	\(3489512452189174333440\)	\([2]\)	\(1548288\)	\(2.8398\)
31920.k1	31920z4	\([0, -1, 0, -28386856, -58203987344]\)	\(617611911727813844500009/1197723879765000\)	\(4905877011517440000\)	\([2]\)	\(1548288\)	\(2.8398\)