Elliptic curve isogeny class with Cremona label 95550jf (LMFDB label 95550.jv)

• Label: 95550jf
• Number of curves: $4$
• Conductor: $95550$
• CM: no
• Rank: $0$

Rank

The elliptic curves in class 95550jf have rank \(0\).

L-function data

Bad L-factors:

Prime	L-Factor
\(2\)	\(1 - T\)
\(3\)	\(1 - T\)
\(5\)	\(1\)
\(7\)	\(1\)
\(13\)	\(1 - T\)

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 - 4 T + 19 T^{2}\)	1.19.ae
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 + 4 T + 29 T^{2}\)	1.29.e
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 95550jf do not have complex multiplication.

Modular form 95550.2.a.jf

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 95550jf

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
95550.jv4	95550jf1	\([1, 0, 0, -353438, -133640508]\)	\(-2656166199049/2658140160\)	\(-4886367682560000000\)	\([2]\)	\(2211840\)	\(2.2818\)	\(\Gamma_0(N)\)-optimal
95550.jv3	95550jf2	\([1, 0, 0, -6625438, -6562440508]\)	\(17496824387403529/6580454400\)	\(12096623120400000000\)	\([2, 2]\)	\(4423680\)	\(2.6284\)
95550.jv2	95550jf3	\([1, 0, 0, -7605438, -4493660508]\)	\(26465989780414729/10571870144160\)	\(19433905477973122500000\)	\([2]\)	\(8847360\)	\(2.9749\)
95550.jv1	95550jf4	\([1, 0, 0, -105997438, -420049332508]\)	\(71647584155243142409/10140000\)	\(18640013437500000\)	\([2]\)	\(8847360\)	\(2.9749\)