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Properties

Label 372232.p
Number of curves $1$
Conductor $372232$
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, 0, 0, -1819, -29818]) E.isogeny_class()
 
Copy content magma:E := EllipticCurve([0, 0, 0, -1819, -29818]); IsogenousCurves(E);
 
Copy content gp:E = ellinit([0, 0, 0, -1819, -29818]) 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 372232.p1 has rank \(1\).

L-function data

Bad L-factors:
Prime L-Factor
\(2\)\(1\)
\(7\)\(1 + T\)
\(17\)\(1\)
\(23\)\(1 - T\)
 
Good L-factors:
Prime L-Factor Isogeny Class over \(\mathbb{F}_p\)
\(3\) \( 1 - 3 T + 3 T^{2}\) 1.3.ad
\(5\) \( 1 - 2 T + 5 T^{2}\) 1.5.ac
\(11\) \( 1 - 2 T + 11 T^{2}\) 1.11.ac
\(13\) \( 1 + 13 T^{2}\) 1.13.a
\(19\) \( 1 - T + 19 T^{2}\) 1.19.ab
\(29\) \( 1 + T + 29 T^{2}\) 1.29.b
$\cdots$$\cdots$$\cdots$
 
See L-function page for more information

Complex multiplication

The elliptic curves in class 372232.p do not have complex multiplication.

Modular form 372232.2.a.p

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);
 
\(q + 3 q^{3} + 2 q^{5} - q^{7} + 6 q^{9} + 2 q^{11} + 6 q^{15} + q^{19} + O(q^{20})\) 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 372232.p

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
372232.p1 372232p1 \([0, 0, 0, -1819, -29818]\) \(2249178948/3703\) \(1095851008\) \([]\) \(331776\) \(0.63080\) \(\Gamma_0(N)\)-optimal