Elliptic curve isogeny class with Cremona label 31680bl (LMFDB label 31680.dw)

• Label: 31680bl
• Number of curves: $4$
• Conductor: $31680$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 31680bl have rank \(1\).

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

See L-function page for more information

Complex multiplication

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

Modular form 31680.2.a.bl

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 31680bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
31680.dw3	31680bl1	\([0, 0, 0, -181512, -29765016]\)	\(885956203616256/15125\)	\(11290752000\)	\([2]\)	\(147456\)	\(1.4708\)	\(\Gamma_0(N)\)-optimal
31680.dw2	31680bl2	\([0, 0, 0, -181692, -29703024]\)	\(55537159171536/228765625\)	\(2732361984000000\)	\([2, 2]\)	\(294912\)	\(1.8174\)
31680.dw4	31680bl3	\([0, 0, 0, -94572, -58243536]\)	\(-1957960715364/29541015625\)	\(-1411344000000000000\)	\([2]\)	\(589824\)	\(2.1640\)
31680.dw1	31680bl4	\([0, 0, 0, -271692, 2804976]\)	\(46424454082884/26794860125\)	\(1280144377847808000\)	\([2]\)	\(589824\)	\(2.1640\)