Elliptic curve isogeny class with Cremona label 63075d (LMFDB label 63075.y)

• Label: 63075d
• Number of curves: $2$
• Conductor: $63075$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 63075d have rank \(1\).

L-function data

Bad L-factors:

Prime	L-Factor
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(29\)	\(1\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(2\)	\( 1 + 2 T + 2 T^{2}\)	1.2.c
\(7\)	\( 1 + T + 7 T^{2}\)	1.7.b
\(11\)	\( 1 - 4 T + 11 T^{2}\)	1.11.ae
\(13\)	\( 1 - 6 T + 13 T^{2}\)	1.13.ag
\(17\)	\( 1 + 17 T^{2}\)	1.17.a
\(19\)	\( 1 - T + 19 T^{2}\)	1.19.ab
\(23\)	\( 1 - 4 T + 23 T^{2}\)	1.23.ae
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 63075d do not have complex multiplication.

Modular form 63075.2.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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

The vertices are labelled with Cremona labels.

Elliptic curves in class 63075d

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
63075.y2	63075d1	\([0, -1, 1, 1402, 88733]\)	\(20480/243\)	\(-3613551675075\)	\([]\)	\(134400\)	\(1.0905\)	\(\Gamma_0(N)\)-optimal
63075.y1	63075d2	\([0, -1, 1, -175208, -28875307]\)	\(-102400/3\)	\(-17426464482421875\)	\([]\)	\(672000\)	\(1.8953\)