Elliptic curve isogeny class with LMFDB label 278080.bm (Cremona label 278080bm)

• Label: 278080.bm
• Number of curves: $4$
• Conductor: $278080$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 278080.bm have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(5\)	\(1 + T\)
\(11\)	\(1 + T\)
\(79\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(3\)	\( 1 + 3 T^{2}\)	1.3.a
\(7\)	\( 1 + 7 T^{2}\)	1.7.a
\(13\)	\( 1 - 2 T + 13 T^{2}\)	1.13.ac
\(17\)	\( 1 + 6 T + 17 T^{2}\)	1.17.g
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 8 T + 23 T^{2}\)	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 278080.bm do not have complex multiplication.

Modular form 278080.2.a.bm

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.

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

Isogeny graph

The vertices are labelled with LMFDB labels.

Elliptic curves in class 278080.bm

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
278080.bm1	278080bm3	\([0, 0, 0, -524588, 146120912]\)	\(121806044811730242/117823995025\)	\(15443426675916800\)	\([4]\)	\(2228224\)	\(2.0273\)
278080.bm2	278080bm4	\([0, 0, 0, -356588, -81171888]\)	\(38257268424094242/423358789975\)	\(55490483319603200\)	\([2]\)	\(2228224\)	\(2.0273\)
278080.bm3	278080bm2	\([0, 0, 0, -40588, 1114512]\)	\(112833156224484/57109050625\)	\(3742698741760000\)	\([2, 2]\)	\(1114112\)	\(1.6807\)
278080.bm4	278080bm1	\([0, 0, 0, 9412, 134512]\)	\(5627940902064/3733984375\)	\(-61177600000000\)	\([2]\)	\(557056\)	\(1.3342\)	\(\Gamma_0(N)\)-optimal