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Properties

Label 87087.c
Number of curves $1$
Conductor $87087$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve([0, 1, 1, 65, 337]) E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 87087.c1 has rank \(1\).

L-function data

 
Bad L-factors:
Prime L-Factor
\(3\)\(1 - T\)
\(7\)\(1 - T\)
\(11\)\(1 - T\)
\(13\)\(1 - T\)
\(29\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(2\) \( 1 + 2 T^{2}\) 1.2.a
\(5\) \( 1 - T + 5 T^{2}\) 1.5.ab
\(17\) \( 1 + T + 17 T^{2}\) 1.17.b
\(19\) \( 1 - 4 T + 19 T^{2}\) 1.19.ae
\(23\) \( 1 + 2 T + 23 T^{2}\) 1.23.c
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 87087.c do not have complex multiplication.

Modular form 87087.2.a.c

Copy content sage:E.q_eigenform(10)
 
\(q + q^{3} - 2 q^{4} + q^{5} + q^{7} + q^{9} + q^{11} - 2 q^{12} + q^{13} + q^{15} + 4 q^{16} - q^{17} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny graph

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

Elliptic curves in class 87087.c

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
87087.c1 87087f1 \([0, 1, 1, 65, 337]\) \(29906468864/60351291\) \(-60351291\) \([]\) \(16896\) \(0.17741\) \(\Gamma_0(N)\)-optimal