Elliptic curve isogeny class with LMFDB label 71478.bl (Cremona label 71478ct)

• Label: 71478.bl
• Number of curves: $4$
• Conductor: $71478$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 71478.bl have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1\)
\(11\)	\(1 - T\)
\(19\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + 2 T + 5 T^{2}\)	1.5.c
\(7\)	\( 1 + 4 T + 7 T^{2}\)	1.7.e
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(23\)	\( 1 + 4 T + 23 T^{2}\)	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 71478.bl do not have complex multiplication.

Modular form 71478.2.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 LMFDB 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 LMFDB labels.

Elliptic curves in class 71478.bl

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
71478.bl1	71478ct4	\([1, -1, 1, -1143716, -470501899]\)	\(4824238966273/66\)	\(2263565518434\)	\([2]\)	\(884736\)	\(1.9266\)
71478.bl2	71478ct2	\([1, -1, 1, -71546, -7324459]\)	\(1180932193/4356\)	\(149395324216644\)	\([2, 2]\)	\(442368\)	\(1.5800\)
71478.bl3	71478ct3	\([1, -1, 1, -39056, -14030395]\)	\(-192100033/2371842\)	\(-81345754035962658\)	\([2]\)	\(884736\)	\(1.9266\)
71478.bl4	71478ct1	\([1, -1, 1, -6566, 5285]\)	\(912673/528\)	\(18108524147472\)	\([2]\)	\(221184\)	\(1.2334\)	\(\Gamma_0(N)\)-optimal