Elliptic curve isogeny class with LMFDB label 31680.bw (Cremona label 31680da)

• Label: 31680.bw
• Number of curves: $4$
• Conductor: $31680$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 31680.bw have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(5\)	\(1 + T\)
\(11\)	\(1 - T\)

Good L-factors:

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

See L-function page for more information

Complex multiplication

The elliptic curves in class 31680.bw do not have complex multiplication.

Modular form 31680.2.a.bw

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 LMFDB numbering.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 31680.bw

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
31680.bw1	31680da4	\([0, 0, 0, -56028, -2772848]\)	\(1628514404944/664335375\)	\(7934779201536000\)	\([2]\)	\(221184\)	\(1.7485\)
31680.bw2	31680da2	\([0, 0, 0, -25788, 1593808]\)	\(158792223184/16335\)	\(195104194560\)	\([2]\)	\(73728\)	\(1.1992\)
31680.bw3	31680da1	\([0, 0, 0, -1488, 28888]\)	\(-488095744/200475\)	\(-149653785600\)	\([2]\)	\(36864\)	\(0.85261\)	\(\Gamma_0(N)\)-optimal
31680.bw4	31680da3	\([0, 0, 0, 11472, -315848]\)	\(223673040896/187171875\)	\(-139723056000000\)	\([2]\)	\(110592\)	\(1.4019\)