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Properties

Label 478800.jw
Number of curves $2$
Conductor $478800$
CM no
Rank $0$
Graph

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Show commands: SageMath
Copy content sage:E = EllipticCurve("jw1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 478800.jw have rank \(0\).

Complex multiplication

The elliptic curves in class 478800.jw do not have complex multiplication.

Modular form 478800.2.a.jw

Copy content sage:E.q_eigenform(10)
 
\(q + q^{7} - 3 q^{11} + 7 q^{13} + 3 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content sage:E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.

Elliptic curves in class 478800.jw

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
478800.jw1 478800jw1 \([0, 0, 0, -5886075, 5752782250]\) \(-483385461758641/26693632000\) \(-1245418094592000000000\) \([]\) \(29859840\) \(2.8057\) \(\Gamma_0(N)\)-optimal
478800.jw2 478800jw2 \([0, 0, 0, 31553925, 11337102250]\) \(74469146542554959/44285662466080\) \(-2066191868017428480000000\) \([]\) \(89579520\) \(3.3550\)