Elliptic curve isogeny class with Cremona label 87360dr (LMFDB label 87360.gt)

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

Rank

The elliptic curves in class 87360dr 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.ae
\(17\)	\( 1 - 6 T + 17 T^{2}\)	1.17.ag
\(19\)	\( 1 + 4 T + 19 T^{2}\)	1.19.e
\(23\)	\( 1 + 4 T + 23 T^{2}\)	1.23.e
\(29\)	\( 1 - 10 T + 29 T^{2}\)	1.29.ak
$\cdots$	$\cdots$	$\cdots$

See L-function page for more information

Complex multiplication

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

Modular form 87360.2.a.dr

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 87360dr

LMFDB label	Cremona label	Weierstrass coefficients	j-invariant	Discriminant	Torsion structure	Modular degree	Faltings height	Optimality
87360.gt4	87360dr1	\([0, 1, 0, -30945, -228225]\)	\(12501706118329/7156531200\)	\(1876041714892800\)	\([2]\)	\(491520\)	\(1.6204\)	\(\Gamma_0(N)\)-optimal
87360.gt2	87360dr2	\([0, 1, 0, -358625, -82606977]\)	\(19458380202497209/47698560000\)	\(12503891312640000\)	\([2, 2]\)	\(983040\)	\(1.9669\)
87360.gt3	87360dr3	\([0, 1, 0, -225505, -144561025]\)	\(-4837870546133689/31603162500000\)	\(-8284579430400000000\)	\([4]\)	\(1966080\)	\(2.3135\)
87360.gt1	87360dr4	\([0, 1, 0, -5734625, -5287650177]\)	\(79560762543506753209/479824800\)	\(125783192371200\)	\([2]\)	\(1966080\)	\(2.3135\)