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Properties

Label 194350.bh
Number of curves $1$
Conductor $194350$
CM no
Rank $0$
Graph

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Show commands: Magma / Pari/GP / SageMath
Copy content comment:Define the isogeny class
 
Copy content sage:E = EllipticCurve([1, -1, 0, -845792, 299324416]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([1, -1, 0, -845792, 299324416]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([1, -1, 0, -845792, 299324416]) 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 194350.bh1 has rank \(0\).

L-function data

Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(5\)\(1\)
\(13\)\(1\)
\(23\)\(1 + T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(3\) \( 1 + 3 T^{2}\) 1.3.a
\(7\) \( 1 - T + 7 T^{2}\) 1.7.ab
\(11\) \( 1 - 3 T + 11 T^{2}\) 1.11.ad
\(17\) \( 1 + 8 T + 17 T^{2}\) 1.17.i
\(19\) \( 1 - 7 T + 19 T^{2}\) 1.19.ah
\(29\) \( 1 - 7 T + 29 T^{2}\) 1.29.ah
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 194350.bh do not have complex multiplication.

Modular form 194350.2.a.bh

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);
 
\(q - q^{2} + q^{4} + q^{7} - q^{8} - 3 q^{9} + 3 q^{11} - q^{14} + q^{16} - 8 q^{17} + 3 q^{18} + 7 q^{19} + O(q^{20})\) 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 194350.bh

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
194350.bh1 194350dk1 \([1, -1, 0, -845792, 299324416]\) \(22180666338225/24117248\) \(72755843563520000\) \([]\) \(3231360\) \(2.1510\) \(\Gamma_0(N)\)-optimal