Elliptic curve isogeny class with Cremona label 63504co (LMFDB label 63504.bi)

• Label: 63504co
• Number of curves: $4$
• Conductor: $63504$
• CM: no
• Rank: $2$

Rank

The elliptic curves in class 63504co have rank \(2\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1\)
\(3\)	\(1\)
\(7\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 - 3 T + 5 T^{2}\)	1.5.ad
\(11\)	\( 1 + 3 T + 11 T^{2}\)	1.11.d
\(13\)	\( 1 - 5 T + 13 T^{2}\)	1.13.af
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 + 5 T + 19 T^{2}\)	1.19.f
\(23\)	\( 1 + 3 T + 23 T^{2}\)	1.23.d
\(29\)	\( 1 - 3 T + 29 T^{2}\)	1.29.ad
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 63504co do not have complex multiplication.

Modular form 63504.2.a.co

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 7 & 21 \\ 3 & 1 & 21 & 7 \\ 7 & 21 & 1 & 3 \\ 21 & 7 & 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 63504co

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
63504.bi4	63504co1	\([0, 0, 0, 2205, -6174]\)	\(3375/2\)	\(-702596063232\)	\([]\)	\(51840\)	\(0.96251\)	\(\Gamma_0(N)\)-optimal
63504.bi3	63504co2	\([0, 0, 0, -33075, -2426382]\)	\(-140625/8\)	\(-227641124487168\)	\([]\)	\(155520\)	\(1.5118\)
63504.bi1	63504co3	\([0, 0, 0, -844515, 298716642]\)	\(-189613868625/128\)	\(-44966148046848\)	\([]\)	\(362880\)	\(1.9355\)
63504.bi2	63504co4	\([0, 0, 0, -668115, 426987666]\)	\(-1159088625/2097152\)	\(-59674754937564168192\)	\([]\)	\(1088640\)	\(2.4848\)