Elliptic curve isogeny class with Cremona label 71400d (LMFDB label 71400.bp)

• Label: 71400d
• Number of curves: $4$
• Conductor: $71400$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 71400d have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 + T\)
\(5\)	\(1\)
\(7\)	\(1 + T\)
\(17\)	\(1 + T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 2 T + 11 T^{2}\)	1.11.c
\(13\)	\( 1 + 4 T + 13 T^{2}\)	1.13.e
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 - 8 T + 23 T^{2}\)	1.23.ai
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 71400d do not have complex multiplication.

Modular form 71400.2.a.d

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 71400d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
71400.bp4	71400d1	\([0, -1, 0, -17666108, 28851244212]\)	\(-152435594466395827792/1646846627220711\)	\(-6587386508882844000000\)	\([2]\)	\(4423680\)	\(3.0026\)	\(\Gamma_0(N)\)-optimal
71400.bp3	71400d2	\([0, -1, 0, -283386608, 1836282085212]\)	\(157304700372188331121828/18069292138401\)	\(289108674214416000000\)	\([2, 2]\)	\(8847360\)	\(3.3492\)
71400.bp2	71400d3	\([0, -1, 0, -284115608, 1826360395212]\)	\(79260902459030376659234/842751810121431609\)	\(26968057923885811488000000\)	\([2]\)	\(17694720\)	\(3.6957\)
71400.bp1	71400d4	\([0, -1, 0, -4534185608, 117517526071212]\)	\(322159999717985454060440834/4250799\)	\(136025568000000\)	\([2]\)	\(17694720\)	\(3.6957\)