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Properties

Label 48450v
Number of curves $1$
Conductor $48450$
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([1, 0, 1, -13451, 815798]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([1, 0, 1, -13451, 815798]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([1, 0, 1, -13451, 815798]) 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 48450v1 has rank \(1\).

L-function data

Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(3\)\(1 - T\)
\(5\)\(1\)
\(17\)\(1 - T\)
\(19\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(7\) \( 1 - 5 T + 7 T^{2}\) 1.7.af
\(11\) \( 1 - T + 11 T^{2}\) 1.11.ab
\(13\) \( 1 - 2 T + 13 T^{2}\) 1.13.ac
\(23\) \( 1 + 4 T + 23 T^{2}\) 1.23.e
\(29\) \( 1 - 9 T + 29 T^{2}\) 1.29.aj
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 48450v do not have complex multiplication.

Modular form 48450.2.a.v

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);
 
\(q - q^{2} + q^{3} + q^{4} - q^{6} - 2 q^{7} - q^{8} + q^{9} + 2 q^{11} + q^{12} + 4 q^{13} + 2 q^{14} + q^{16} + q^{17} - q^{18} + q^{19} + O(q^{20})\) 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 48450v

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
48450.q1 48450v1 \([1, 0, 1, -13451, 815798]\) \(-688939335625/339351552\) \(-132559200000000\) \([]\) \(190080\) \(1.4151\) \(\Gamma_0(N)\)-optimal