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Properties

Label 417600.r
Number of curves $1$
Conductor $417600$
CM no
Rank $1$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve([0, 0, 0, -56167500, 162042950000]) E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curve 417600.r1 has rank \(1\).

Complex multiplication

The elliptic curves in class 417600.r do not have complex multiplication.

Modular form 417600.2.a.r

Copy content sage:E.q_eigenform(10)
 
\(q - 4 q^{7} - 2 q^{11} - 2 q^{17} - 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny graph

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

Elliptic curves in class 417600.r

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
417600.r1 417600r1 \([0, 0, 0, -56167500, 162042950000]\) \(-10500536779225/1522152\) \(-2840700948480000000000\) \([]\) \(30965760\) \(3.1315\) \(\Gamma_0(N)\)-optimal