Elliptic curve isogeny class with LMFDB label 87360.fs (Cremona label 87360gz)

• Label: 87360.fs
• Number of curves: $4$
• Conductor: $87360$
• CM: no
• Rank: $1$

Rank

The elliptic curves in class 87360.fs have rank \(1\).

L-function data

Bad L-factors:

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

Good L-factors:

Prime	L-Factor	Isogeny Class over \(\mathbb{F}_p\)
\(11\)	\( 1 + 4 T + 11 T^{2}\)	1.11.e
\(17\)	\( 1 - 2 T + 17 T^{2}\)	1.17.ac
\(19\)	\( 1 + 19 T^{2}\)	1.19.a
\(23\)	\( 1 + 23 T^{2}\)	1.23.a
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

The elliptic curves in class 87360.fs do not have complex multiplication.

Modular form 87360.2.a.fs

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 87360.fs

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
87360.fs1	87360gz4	\([0, 1, 0, -1546305, -740009025]\)	\(1559802282754777489/1481059636875\)	\(388250897448960000\)	\([2]\)	\(1769472\)	\(2.2969\)
87360.fs2	87360gz2	\([0, 1, 0, -119425, -5736577]\)	\(718576775407009/362361861225\)	\(94990987748966400\)	\([2, 2]\)	\(884736\)	\(1.9503\)
87360.fs3	87360gz1	\([0, 1, 0, -65345, 6344895]\)	\(117713838907729/1322517105\)	\(346689923973120\)	\([2]\)	\(442368\)	\(1.6038\)	\(\Gamma_0(N)\)-optimal
87360.fs4	87360gz3	\([0, 1, 0, 442175, -43813057]\)	\(36472485598112591/24291459037755\)	\(-6367860237993246720\)	\([2]\)	\(1769472\)	\(2.2969\)