Elliptic curve isogeny class with Cremona label 75504cp (LMFDB label 75504.bp)

• Label: 75504cp
• Number of curves: $4$
• Conductor: $75504$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 75504cp have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1 - T\)
\(11\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 2 T + 5 T^{2}\)	1.5.ac
\(7\)	\( 1 - 3 T + 7 T^{2}\)	1.7.ad
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - 3 T + 19 T^{2}\)	1.19.ad
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 8 T + 29 T^{2}\)	1.29.ai
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 75504cp do not have complex multiplication.

Modular form 75504.2.a.cp

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 75504cp

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
75504.bp4	75504cp1	\([0, 1, 0, -298184, 72762996]\)	\(-404075127457/82223856\)	\(-596642105586548736\)	\([2]\)	\(829440\)	\(2.1332\)	\(\Gamma_0(N)\)-optimal
75504.bp3	75504cp2	\([0, 1, 0, -4983304, 4280000756]\)	\(1886079023633377/59629284\)	\(432688799712559104\)	\([2, 2]\)	\(1658880\)	\(2.4798\)
75504.bp2	75504cp3	\([0, 1, 0, -5196264, 3894032052]\)	\(2138362647385537/333926700822\)	\(2423076946063045189632\)	\([2]\)	\(3317760\)	\(2.8264\)
75504.bp1	75504cp4	\([0, 1, 0, -79732264, 274004148020]\)	\(7725203825376001537/7722\)	\(56033255596032\)	\([2]\)	\(3317760\)	\(2.8264\)