Properties

Label 108300bu
Number of curves $1$
Conductor $108300$
CM no
Rank $1$
Graph

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Show commands: Magma / Pari/GP / SageMath
Copy content comment:Define the isogeny class
 
Copy content sage:E = EllipticCurve([0, 1, 0, -57158, -60956187]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([0, 1, 0, -57158, -60956187]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([0, 1, 0, -57158, -60956187]) ellisomat(E)
 

Rank

Copy content comment:Mordell-Weil rank
 
Copy content sage:E.rank()
 
Copy content gp:[lower,upper] = ellrank(E)
 
Copy content magma:Rank(E);
 

The elliptic curve 108300bu1 has rank \(1\).

L-function data

Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(3\)\(1 - T\)
\(5\)\(1\)
\(19\)\(1\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 + T + 7 T^{2}\) 1.7.b
\(11\) \( 1 - T + 11 T^{2}\) 1.11.ab
\(13\) \( 1 + 4 T + 13 T^{2}\) 1.13.e
\(17\) \( 1 - 3 T + 17 T^{2}\) 1.17.ad
\(23\) \( 1 + 4 T + 23 T^{2}\) 1.23.e
\(29\) \( 1 - 8 T + 29 T^{2}\) 1.29.ai
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 108300bu do not have complex multiplication.

Modular form 108300.2.a.bu

Copy content comment:q-expansion of modular form
 
Copy content sage:E.q_eigenform(20)
 
Copy content gp:Ser(ellan(E,20),q)*q
 
Copy content magma:ModularForm(E);
 
\(q + q^{3} - 4 q^{7} + q^{9} - 2 q^{11} - 6 q^{13} + 5 q^{17} + O(q^{20})\) Copy content Toggle raw display

Isogeny graph

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

Elliptic curves in class 108300bu

Copy content comment:List of curves in the isogeny class
 
Copy content sage:E.isogeny_class().curves
 
Copy content magma:IsogenousCurves(E);
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
108300.bl1 108300bu1 \([0, 1, 0, -57158, -60956187]\) \(-4864/375\) \(-1592209035093750000\) \([]\) \(2068416\) \(2.1723\) \(\Gamma_0(N)\)-optimal