Elliptic curve isogeny class with Cremona label 63504bf (LMFDB label 63504.bm)

• Label: 63504bf
• Number of curves: $2$
• Conductor: $63504$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 63504bf have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(5\)	\( 1 + T + 5 T^{2}\)	1.5.b
\(11\)	\( 1 - 3 T + 11 T^{2}\)	1.11.ad
\(13\)	\( 1 + T + 13 T^{2}\)	1.13.b
\(17\)	\( 1 + 3 T + 17 T^{2}\)	1.17.d
\(19\)	\( 1 - 5 T + 19 T^{2}\)	1.19.af
\(23\)	\( 1 + T + 23 T^{2}\)	1.23.b
\(29\)	\( 1 - 9 T + 29 T^{2}\)	1.29.aj
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 63504.2.a.bf

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 63504bf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
63504.bm2	63504bf1	\([0, 0, 0, -315, 1386]\)	\(23625/8\)	\(1170505728\)	\([]\)	\(20736\)	\(0.44230\)	\(\Gamma_0(N)\)-optimal
63504.bm1	63504bf2	\([0, 0, 0, -10395, -407862]\)	\(10481625/2\)	\(23702740992\)	\([]\)	\(62208\)	\(0.99161\)