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Properties

Label 71630h
Number of curves $1$
Conductor $71630$
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, -1, 0, 5, 11]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([1, -1, 0, 5, 11]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([1, -1, 0, 5, 11]) 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 71630h1 has rank \(1\).

L-function data

Bad L-factors:
Prime L-Factor
\(2\)\(1 + T\)
\(5\)\(1 + T\)
\(13\)\(1 + T\)
\(19\)\(1 - T\)
\(29\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(3\) \( 1 + T + 3 T^{2}\) 1.3.b
\(7\) \( 1 - 3 T + 7 T^{2}\) 1.7.ad
\(11\) \( 1 + 11 T^{2}\) 1.11.a
\(17\) \( 1 + 2 T + 17 T^{2}\) 1.17.c
\(23\) \( 1 + 4 T + 23 T^{2}\) 1.23.e
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 71630h do not have complex multiplication.

Modular form 71630.2.a.h

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);
 
\(q - q^{2} + 3 q^{3} + q^{4} - q^{5} - 3 q^{6} + q^{7} - q^{8} + 6 q^{9} + q^{10} + 3 q^{12} + q^{13} - q^{14} - 3 q^{15} + q^{16} - 2 q^{17} - 6 q^{18} - q^{19} + O(q^{20})\) 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 71630h

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
71630.t1 71630h1 \([1, -1, 0, 5, 11]\) \(12326391/71630\) \(-71630\) \([]\) \(13376\) \(-0.38644\) \(\Gamma_0(N)\)-optimal