Elliptic curve isogeny class with LMFDB label 75504.cr (Cremona label 75504da)

• Label: 75504.cr
• Number of curves: $4$
• Conductor: $75504$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 75504.cr have rank \(1\).

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
\(7\)	\( 1 - 4 T + 7 T^{2}\)	1.7.ae
\(17\)	\( 1 + 2 T + 17 T^{2}\)	1.17.c
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 2 T + 29 T^{2}\)	1.29.ac
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 75504.2.a.cr

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 75504.cr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
75504.cr1	75504da4	\([0, 1, 0, -25684952, -49785908460]\)	\(258252149810350513/1938176193096\)	\(14064014765331836338176\)	\([2]\)	\(6635520\)	\(3.0800\)
75504.cr2	75504da2	\([0, 1, 0, -2685272, 399393300]\)	\(295102348042033/161237583936\)	\(1169990514422759817216\)	\([2, 2]\)	\(3317760\)	\(2.7334\)
75504.cr3	75504da1	\([0, 1, 0, -2065752, 1140587028]\)	\(134351465835313/205590528\)	\(1491829396988755968\)	\([2]\)	\(1658880\)	\(2.3868\)	\(\Gamma_0(N)\)-optimal
75504.cr4	75504da3	\([0, 1, 0, 10402088, 3158208788]\)	\(17154149157653327/10519679024712\)	\(-76334092667690252009472\)	\([2]\)	\(6635520\)	\(3.0800\)